Fraudulent Inventor
Q. Professor Lipshultz was showing off his new inventions to a prospective investor. He told the investor that he had developed machines which would allow scientists to study the motion of gas molecules. His explanation of the machines was as follows:
"The first unit will take in any gas and completely dry it, removing all traces of liquid. Right now it is removing water vapor from air...and now you can see the "DRY" light has come on.
The second unit removes all but one molecule from the chamber. There you see the "READY" light, indicating that only a single molecule remains.
The third unit will analyze the contents of the chamber, determining exactly what chemicals are in the chamber, and in what quantity. And as you can see on the screen, the unit indicates 'Air: 1 molecule'.
The final machine will trace the exact path that the molecule takes as it bounces around the chamber. The path is represented by the lines on this computer screen."
"I'm sorry," said the investor, "but you're obviously lying to me. I can accept the fact that three of the four machines COULD work as you say, but one of them is obviously a fake."
Which machine was the fake?
Answer
The third unit, which analyzed the contents of the chamber, is definitely a fake. "Air" is a name that we give to the combination of gasses that make up our atmosphere. It is made up of oxygen, nitrogen, carbon dioxide, and trace amounts of several other chemicals. Because of this, there is no such thing as one molecule of air. Assuming that there is only one molecule in the chamber, it would either be oxygen, nitrogen, or one of the other chemicals. A piece of analysis equipment would never call it "air".
Joe Thunder
Q. As his name would suggest, Joe was not a meek, quiet fellow. In fact he had such difficulty keeping quiet, both his local and university library banned him. His roommate, being a music major and a sound engineer, said he could solve his problem, but Joe would need to trust him. He gave Joe his 75-watt ghetto blaster, a CD, fake mustache, and a long blond wig. Joe, who is sceptical but intrigued, decided to give it a shot. Joe, disguised as one of the professors, entered the university library. He placed the CD player on the table in front of him; loaded the CD; cranked the volume full and braced himself as he turned it on. Surprisingly there was only a very very faint sshh. Joe then realized that he couldn't hear anything at all. He spoke normally, and then yelled, but no one reacted. Awesome, he thought as he began flailing his arms around and shouting as loud as he could. Unfortunately, the librarian, seeing him moving but hearing nothing, assumed he was choking and performed the Heimlich maneuver on him, knocking his wig off, causing the librarian to perform the hind kick maneuver right out the door. Poor Joe.
But what had his roommate done? What was on that mysterious CD that made everything quiet?
Answer
Most airline pilots could tell you. Joe's roommate used the same technology that airline and fighter pilots have in their noise cancelling headsets. It works like this; the CD had a low frequency sound (below the 20 Hz which humans can't hear) recorded on it. As long as the volume of the low frequency is louder than your voice or other noise, you hear almost nothing for the low sounds (which humans can't hear) and drown out other sounds. I heard that when this was first discovered that libraries actually used this concept to create quiet until they realized that even though humans couldn't hear the low sound, if loud enough, it would still damage the ears.
The Intruder
Q.
Emily was sitting at her study table, home alone, on a cold and stormy night. Her parents had taken a flight earlier in the morning to Australia as her grandmother had passed away. She had wanted to follow her parents but she had an important English examination the next day which she could not miss.
The storm was getting heavier by the minute and the wind was howling outside. All this noise made it very hard for her to concentrate. She was on the verge of dozing off when she was shaken alert by a sudden "THUD!" She dismissed it as a window which had been slammed shut by the wind.
She tried to concentrate on her books when she heard faint footsteps. Emily got out of her room and looked around when suddenly, without warning, she was grabbed by the neck. She tried to scream but it came out as a mere whimper as the intruder was pressing hard against her throat with his arm. She tried to free herself from his grip but to no avail.
"Give me all your money!" growled the man who had grabbed her from behind.
"Th-there is none h-here! Please ll-let me go!" cried Emily.
"Don't LIE TO ME!" screamed the increasingly agitated man. She felt the man strengthen his grip around her neck. She said nothing and a few seconds passed by in silence. Suddenly the phone rang which alerted both of them.
"People will get suspicious if I don't answer the phone," said Emily, with a controlled voice. The intruder let her go.
"Alright, but NO funny business, or ELSE!" said the nervous intruder. Emily walked toward the phone. She took a deep breath and calmed herself. She picked up the phone.
"Hey Em! How's the revision going?" said the caller.
"Hey Anna. Thanks for the call. Hey you know those Science notes I lent you last week? Well I really need them back. It would be a great help to me. It's an emergency, so if you could give me them tomorrow it would be great. Please hurry in finding the notes. I need to get back to my books now. Bye," Emily said. She hung up the phone.
"It was wise of you not to say anything," said the intruder, although he was more than a bit confused by her conversation.
"Now TELL ME WHERE THE MONEY IS KEPT!" screamed the thief.
"It...it's...in my dad's room. The first room on the right. Third drawer," said Emily.
"SHOW me!" said the man, and removed his grip around her neck. She took a big gulp of air and nearly fell. She swallowed hard and said a silent prayer. She walked slowly, in silence, toward her father's room. All of a sudden, they heard police sirens. The intruder froze in his footsteps. He ran to the nearest window and jumped out of it.
Emily ran outside in time to see the intruder being escorted into the car. She saw Anna and she ran toward her and hugged her.
"Smart kids," said the policeman.
What had happened?
The storm was getting heavier by the minute and the wind was howling outside. All this noise made it very hard for her to concentrate. She was on the verge of dozing off when she was shaken alert by a sudden "THUD!" She dismissed it as a window which had been slammed shut by the wind.
She tried to concentrate on her books when she heard faint footsteps. Emily got out of her room and looked around when suddenly, without warning, she was grabbed by the neck. She tried to scream but it came out as a mere whimper as the intruder was pressing hard against her throat with his arm. She tried to free herself from his grip but to no avail.
"Give me all your money!" growled the man who had grabbed her from behind.
"Th-there is none h-here! Please ll-let me go!" cried Emily.
"Don't LIE TO ME!" screamed the increasingly agitated man. She felt the man strengthen his grip around her neck. She said nothing and a few seconds passed by in silence. Suddenly the phone rang which alerted both of them.
"People will get suspicious if I don't answer the phone," said Emily, with a controlled voice. The intruder let her go.
"Alright, but NO funny business, or ELSE!" said the nervous intruder. Emily walked toward the phone. She took a deep breath and calmed herself. She picked up the phone.
"Hey Em! How's the revision going?" said the caller.
"Hey Anna. Thanks for the call. Hey you know those Science notes I lent you last week? Well I really need them back. It would be a great help to me. It's an emergency, so if you could give me them tomorrow it would be great. Please hurry in finding the notes. I need to get back to my books now. Bye," Emily said. She hung up the phone.
"It was wise of you not to say anything," said the intruder, although he was more than a bit confused by her conversation.
"Now TELL ME WHERE THE MONEY IS KEPT!" screamed the thief.
"It...it's...in my dad's room. The first room on the right. Third drawer," said Emily.
"SHOW me!" said the man, and removed his grip around her neck. She took a big gulp of air and nearly fell. She swallowed hard and said a silent prayer. She walked slowly, in silence, toward her father's room. All of a sudden, they heard police sirens. The intruder froze in his footsteps. He ran to the nearest window and jumped out of it.
Emily ran outside in time to see the intruder being escorted into the car. She saw Anna and she ran toward her and hugged her.
"Smart kids," said the policeman.
What had happened?
Answer
Emily had used the mute button during her conversation with Anna so that all Anna heard was: "call...help...emergency...please hurry". Anna, sensing something was wrong, called the police and told them Emily's address. The police were able to come to Emily's house in time to catch the perpetrator.
Chess League !!!
Q. Four players - Anand, Karpov, Ivanchuk, and Polgar - participated in a chess competition in which each player played exactly one game with each of the other three players. At the end of the competition the results were as follows :-
1) Karpov won against Ivanchuk, who did not win against Anand.
2) The number of games won by Anand is equal to the number of games won by Ivanchuk.
3) No game ended in a draw.
Then which of the following definitely is true :-
a) Ivanchuk lost to Polgar.
b) Anand lost to Karpov.
c) Polgar lost to Anand.
d) Karpov lost to Polgar.
Ans. The given observations about the individual Round Robin games are as follows:
1) Karpov won against Ivanchuk, who did not win against Anand.
2) The number of games won by Anand is equal to the number of games won by Ivanchuk.
3) No game ended in a draw.
Let us represent Anand, Polgar, Karpov and Ivanchuk by A, P, K and I respectively.
The from the given data we have
Game Winner
A-K
A-P
A-I A
K-P
K-I I
I-P
since Ivanchuk lost both the games against Karpov and Anand from observation 1.
Now from observation 1, Anand has definitely won one game since he beat Ivanchuk. From observation 2, the number of games won by Anand is equal to the number of games won by Ivanchuk. Since Ivanchuk has lost both games, he should at least win the last game so that the number of games won by him is equal to those won by Anand. Also since Anand has won one game, he cannot win games against Karpov and Polgar since Ivanchuk cannot equal him then, after having lost two out of three games. Hence Anand must lose to Karpov and Polgar and Ivanchuk must win against Polgar.
Hence among the given statement b which suggests that Anand lost to Karpov must definitely be true.
Kebab Line Up
Q.
Four men are in a line at the Madadian Police station, charged with unlicensed kebab breeding.
The men are Mad Ade, Buster Artery, Cliff Hedge and Donny Moe - and they are standing in a straight line.
One man is fair, handsome and unscarred.
Two men who are not fair, are each standing next to Mad Ade
Buster Artery is the only man standing next to exactly one handsome man.
Cliff Hedge is the only man not standing next to exactly one scarred man.
Who is fair, handsome and unscarred?
The men are Mad Ade, Buster Artery, Cliff Hedge and Donny Moe - and they are standing in a straight line.
One man is fair, handsome and unscarred.
Two men who are not fair, are each standing next to Mad Ade
Buster Artery is the only man standing next to exactly one handsome man.
Cliff Hedge is the only man not standing next to exactly one scarred man.
Who is fair, handsome and unscarred?
Ans. Cliff Hedge is fair, handsome and unscarred.
From (2), both the men standing next to Mad Ade are not fair. Also, exactly one man is fair, handsome and unscarred. Hence, there are two cases:
Case 1 :: ? (N, ?, ?) : Mad Ade (Y, Y, N) : ? (N, ?, ?) : ? (?, ?, ?)
Case 2 :: ? (N, ?, ?) : Mad Ade (?, ?, ?) : ? (N, ?, ?) : ? (Y, Y, N)
Note the representation - Name (Fair, Handsome, Scarred). "Y" stands for Yes and "N" stands for No. Mad Ade (Y, Y, N) means Mad Ade is Fair, Handsome and Unscarred.(oh, how true this is..NOT)
It is clear that either Mad Ade or the man at the extreme right is fair, handsome and unscarred.
From (4), it is deduced that Cliff Hedge is standing next to unscarred man and each of the other men standing next to exactly one scarred man.
Case 1 :: Cliff Hedge (N, ?, N) : Mad Ade (Y, Y, N) : ? (N, ?, Y) : ? (?, ?, Y)
Case 2 :: ? (N, ?, Y) : Mad Ade (?, ?, Y) : ? (N, ?, N) : Cliff Hedge (Y, Y, N)
From (3), Buster Artery is the only man standing next to exactly one handsome man. But in Case 1, Cliff Hedge is standing next to exactly one handsome man. Hence, Case 1 is not possible and Case 2 is the correct one.
Case 2 :: ? (N, ?, Y) : Mad Ade (?, ?, Y) : ? (N, ?, N) : Cliff Hedge (Y, Y, N)
Again from (3) and (4), there are 2 possibilities as shown below.
Case 2a :: Donny Moe (N, N, Y) : Mad Ade (?, N, Y) : Buster Artery (N, N, N) : Cliff Hedge (Y, Y, N)
Case 2b :: Buster Artery (N, N, Y) : Mad Ade (?, Y, Y) : Donny Moe (N, N, N) : Cliff Hedge (Y, Y, N)
Thus, Cliff Hedge is fair, handsome and unscarred. Also, Mad Ade may be either fair or not fair.
From (2), both the men standing next to Mad Ade are not fair. Also, exactly one man is fair, handsome and unscarred. Hence, there are two cases:
Case 1 :: ? (N, ?, ?) : Mad Ade (Y, Y, N) : ? (N, ?, ?) : ? (?, ?, ?)
Case 2 :: ? (N, ?, ?) : Mad Ade (?, ?, ?) : ? (N, ?, ?) : ? (Y, Y, N)
Note the representation - Name (Fair, Handsome, Scarred). "Y" stands for Yes and "N" stands for No. Mad Ade (Y, Y, N) means Mad Ade is Fair, Handsome and Unscarred.(oh, how true this is..NOT)
It is clear that either Mad Ade or the man at the extreme right is fair, handsome and unscarred.
From (4), it is deduced that Cliff Hedge is standing next to unscarred man and each of the other men standing next to exactly one scarred man.
Case 1 :: Cliff Hedge (N, ?, N) : Mad Ade (Y, Y, N) : ? (N, ?, Y) : ? (?, ?, Y)
Case 2 :: ? (N, ?, Y) : Mad Ade (?, ?, Y) : ? (N, ?, N) : Cliff Hedge (Y, Y, N)
From (3), Buster Artery is the only man standing next to exactly one handsome man. But in Case 1, Cliff Hedge is standing next to exactly one handsome man. Hence, Case 1 is not possible and Case 2 is the correct one.
Case 2 :: ? (N, ?, Y) : Mad Ade (?, ?, Y) : ? (N, ?, N) : Cliff Hedge (Y, Y, N)
Again from (3) and (4), there are 2 possibilities as shown below.
Case 2a :: Donny Moe (N, N, Y) : Mad Ade (?, N, Y) : Buster Artery (N, N, N) : Cliff Hedge (Y, Y, N)
Case 2b :: Buster Artery (N, N, Y) : Mad Ade (?, Y, Y) : Donny Moe (N, N, N) : Cliff Hedge (Y, Y, N)
Thus, Cliff Hedge is fair, handsome and unscarred. Also, Mad Ade may be either fair or not fair.
Half a Clock
Q. One evening Mad Ade sat at home waiting for his favourite Kebab shop, "The Sweaty Chef", to open. He kept glancing as his clock (a regular analog clock face with the numerals 1 to 12 correctly positioned), waiting for opening time. Mad Ade noticed that he could draw a straight line to split the clock face in half in such a way that the sum of the numbers on one side of the line would equal the sum of the numbers on the other side of the line?
Where could Mad Ade draw the line, and what is the total of numbers on either side?
Where could Mad Ade draw the line, and what is the total of numbers on either side?
Ans. If Mad Ade was to draw a straight line that begins on the left side of the clock face between 9 and 10 and cuts across the clock face to the right side between 3 and 4.
The sum of the numbers above the line equals 39, and the sum of the numbers below the line equals 39.
The sum of the numbers above the line equals 39, and the sum of the numbers below the line equals 39.
Opposite Words
Q. In the following code, each symbol stands for one of five letters.
@ stands for E, M, J, O, or A
% stands for R, L, A, C, or Y
$ stands for G, W, F, A, or R
) stands for R, Q, U, S, or E
The four letter code word, $@%), can be translated into two English words that are opposites. What are the two words?
@ stands for E, M, J, O, or A
% stands for R, L, A, C, or Y
$ stands for G, W, F, A, or R
) stands for R, Q, U, S, or E
The four letter code word, $@%), can be translated into two English words that are opposites. What are the two words?
Ans. Fore and Rear.
Q. Adam, Billy, Caroline, and David each have an A in their favorite subject. Each student has only one A and it is in either Calculus, Biology, Physics, or English. Each student's favorite class is taken during a different time from first to fourth period, and there is only one A per period. Match the student to their favorite class and the period in which the class is taken.
1) Adam's class is after Physics and before Biology.
2) Caroline has an A in Biology, so she tutors Billy during their free 4th period.
3) David is grounded for failing Physics 1st period.
4) The student with the A in English has the class 4th period.
Ans.
Adam - Calculus, 2nd period
Billy - Physics, 1st period
Caroline - Biology, 3rd period
David - English, 4th period
The King and the Poison
Q.
In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. The king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom's pharmacist and the kingdom's treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one's poison, then his own, and the one that will survive, will be the one that had the stronger poison.
The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer's plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn't get what he wanted.
What exactly happened there?
The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer's plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn't get what he wanted.
What exactly happened there?
Ans. The treasurer's plan was to drink a weak poison prior to the meeting with the king, and then he would drink the pharmacist's strong poison, which would neutralize the weak poison. As his own poison he would bring water, which will have no effect on him, but the pharmacist who would drink the water, and then his poison would surely die. When the pharmacist figured out this plan, he decided to bring water as well. So the treasurer who drank poison earlier, drank the pharmacist's water, then his own water, and died of the poison he drank before. The pharmacist would drink only water, so nothing will happen to him. And because both of them brought the king water, he didn't get a strong poison like he wanted.
Super Computer
A man goes to his physician and is shocked to find that he has been replaced by a super-computer. The computer asks him his ailments and the man says he has a sore elbow. A drawer pops out and he is asked to urinate in it. After a few bleeps and flashing lights the computer decides he has tennis elbow.
The man is annoyed and decides to get one over on this machine so he asks his wife for a urine sample. He then mixes this with urine from his dog and his small son and to top it off, adds some of his sperm. He takes it to the computer-physician who again asks him for a sample. He places the urine/sperm sample in the drawer and the computer makes its usual display of bleeps and flashes before telling him that his wife is pregnant, his dog has rabies, his son has chicken pox and if he doesn't stop masturbating he'll never get rid of his tennis elbow
Spell Checker
I halve a spelling checker,
It came with my pea see.
It plainly marks four my revue
Mistakes I dew knot sea.
Eye strike a key and type a word
And weight four it two say
Weather eye am wrong oar write
It shows me strait aweigh.
As soon as a mist ache is maid
It nose bee fore two long
And eye can put the era rite
Its rarely ever wrong.
I've scent this massage threw it,
And I'm shore your pleased too no
Its letter prefect in every weigh;
My checker tolled me sew
BEER TROUBLESHOOTING
SYMPTOM: Feet cold and wet.
FAULT: Glass being held at incorrect angle.
ACTION: Rotate glass so that open end points toward
ceiling.
FAULT: Glass being held at incorrect angle.
ACTION: Rotate glass so that open end points toward
ceiling.
SYMPTOM: Feet warm and wet.
FAULT: Improper bladder control.
ACTION: Stand next to nearest dog, complain about house
training.
FAULT: Improper bladder control.
ACTION: Stand next to nearest dog, complain about house
training.
SYMPTOM: Beer unusually pale and tasteless.
FAULT: Glass empty.
ACTION: Get someone to buy you another beer.
FAULT: Glass empty.
ACTION: Get someone to buy you another beer.
SYMPTOM: Opposite wall covered with fluorescent lights.
FAULT: You have fallen over backward.
ACTION: Have yourself leashed to bar.
FAULT: You have fallen over backward.
ACTION: Have yourself leashed to bar.
SYMPTOM: Mouth contains cigarette butts.
FAULT: You have fallen forward.
ACTION: See above.
FAULT: You have fallen forward.
ACTION: See above.
SYMPTOM: Beer tasteless, front of your shirt is wet.
FAULT: Mouth not open, or glass applied to wrong part of
face.
ACTION: Retire to restroom, practice in mirror.
FAULT: Mouth not open, or glass applied to wrong part of
face.
ACTION: Retire to restroom, practice in mirror.
SYMPTOM: Floor blurred.
FAULT: You are looking through bottom of empty glass.
ACTION: Get someone to buy you another beer.
FAULT: You are looking through bottom of empty glass.
ACTION: Get someone to buy you another beer.
SYMPTOM: Floor moving.
FAULT: You are being carried out.
ACTION: Find out if you are being taken to another bar.
FAULT: You are being carried out.
ACTION: Find out if you are being taken to another bar.
SYMPTOM: Room seems unusually dark.
FAULT: Bar has closed.
ACTION: Confirm home address with bartender.
FAULT: Bar has closed.
ACTION: Confirm home address with bartender.
SYMPTOM: Taxi suddenly takes on colorful aspect and
textures.
FAULT: Beer consumption has exceeded personal
limitations.
ACTION: Cover mouth.
textures.
FAULT: Beer consumption has exceeded personal
limitations.
ACTION: Cover mouth.
SYMPTOM: Everyone looks up to you and smiles.
FAULT: You are dancing on the table.
ACTION: Fall on somebody cushy-looking.
FAULT: You are dancing on the table.
ACTION: Fall on somebody cushy-looking.
SYMPTOM: Beer is crystal-clear.
FAULT: It's water. Somebody is trying to sober you up.
ACTION: Punch him.
FAULT: It's water. Somebody is trying to sober you up.
ACTION: Punch him.
SYMPTOM: Hands hurt, nose hurts, mind unusually clear.
FAULT: You have been in a fight.
ACTION: Apologize to everyone you see, just in case it was
them.
FAULT: You have been in a fight.
ACTION: Apologize to everyone you see, just in case it was
them.
SYMPTOM: Don't recognize anyone, don't recognize the room
you're in.
FAULT: You've wandered into the wrong party.
ACTION: See if they have free beer.
you're in.
FAULT: You've wandered into the wrong party.
ACTION: See if they have free beer.
SYMPTOM: Your singing sounds distorted.
FAULT: The beer is too weak.
ACTION: Have more beer until your voice improves.
FAULT: The beer is too weak.
ACTION: Have more beer until your voice improves.
SYMPTOM: Don't remember the words to the song.
FAULT: Beer is just right.
ACTION: Play air guitar.
FAULT: Beer is just right.
ACTION: Play air guitar.
Bicycles or Tricycles ?
Q. Last weekend, I went to play in the nearby park. It was real fun! I rode my new bicycle that Mom had gifted me on my birthday.
On reaching the park, I saw that there were a total of 8 bicycles and tricycles. If the total number of wheels was 20, how many tricycles were there?
Ans. Assuming 2 wheels for each cycle, 8 cycles will have 16 wheels. But, there are 20 − 16 = 4 extra wheels.
As bicycles have 2 wheels and tricycles have 3 wheels, there is 1 extra wheel per tricycle in the park. Thus, the 4 extra wheels belong to 4 tricycles.
Q. 1. A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 2 hours to fill the tank with the large inlet pipe. On the other hand, it takes 4 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 6 hours.
What fraction of the tank (initially empty) will be filled in 0.43 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
Ans.
In one hour,
the large inlet pipe fills 1 / 2 of the tank;
the small inlet pipe fills 1 / 4 of the tank;
the outlet pipe empties 1 / 6 of the tank; and therefore
all three pipes together fill [ (1 / 2) + (1 / 4) − (1 / 6) ] of the tank.
Fraction of the tank that will be filled in 0.43 hours =
0.43 [ (1 / 2) + (1 / 4) − (1 / 6) ] = 0.25.
Speeding Away
Q. The drive from Oakland to Pinewood was a tricky one. I covered the uphill distance of 55 miles at 42 miles per hour. The return journey from Pinewood to Oakland was downhill, and I managed to drive at 56 miles per hour. What was my average speed for the entire journey?
Ans. It it important to note that
| Average speed = Total distance / Total time. |
Total distance = 2 × 55 miles.
Time for uphill journey (from Oakland to Pinewood) = 55 / 42 hours.
Time for downhill journey (from Pinewood to Oakland) = 55 / 56 hours.
Total time = (55 / 42) + (55 / 56) = 2 × 55 / 48 hours.
Average speed = Total distance / Total time = 48 miles per hour.
Grandpa Age
Q.
Grandpa:
"My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?"
Ans. Grandpa:
"This problem is conveniently solved by writing down the necessary equations. Note that there are 12 months in a year, 52 weeks in a year, and 365 days in a year.
Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,
365g = 52s.
Since my grandson is 12g months old,
12g = m.
Since my grandson, my son and I together are 100 years,
g + s + m = 100.
The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.
m / 12 + 365 m / (52 × 12) + m = 100 or
52 m + 365 m + 624 m = 624 × 100 or
m = 624 × 100 / 1041 = 60.
So, I am 60 years old."
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