DAY 237
TWO CARS
Credit: Doug McKay in Parade Magazine--Ask Marilyn by Marilyn Vos Savant
Two cars depart from the same spot for the same destination. One travels at 60 miles per hour, and the other at 65 miles per hour. The faster car arrives at the destination one hour before the slower one. How far did they travel?
Answer:
780 miles.........The faster car gains five miles on the slower one each hour. Since the slower car is traveling at 60 mph, or one mile per minute, it takes the slower car five minutes to make up this distance. So the faster car gains five minutes on the slower car for every hour it travels. To gain an hour, it must travel 12 hours (60 = 5 X 12). 65 X 12 = 780.
Wednesday, 28 April 2010
Tuesday, 27 April 2010
DAY 236
Two youngsters were running as hard as they could. They averaged 6 miles per hour, and then had to rest. On the way back, they averaged only 4 miles per hour for the same distance. Not counting resting time, what was their average speed?
Answer:
4.8 miles per hour.............The apparent answer of 5 miles per hour is wrong. The answer is obtained by dividing the distance covered by the time elapsed, and any distance will do. For example, to run 12 miles would take 2 hours out and 3 hours back. This means it would take them 5 hours to run 24 miles.
Two youngsters were running as hard as they could. They averaged 6 miles per hour, and then had to rest. On the way back, they averaged only 4 miles per hour for the same distance. Not counting resting time, what was their average speed?
Answer:
4.8 miles per hour.............The apparent answer of 5 miles per hour is wrong. The answer is obtained by dividing the distance covered by the time elapsed, and any distance will do. For example, to run 12 miles would take 2 hours out and 3 hours back. This means it would take them 5 hours to run 24 miles.
DAY 235
NO PENCIL--NO PAPER
Credit: Mike Androtti---Parade Magazine---Ask Marilyn by Marilyn Vos Savant
Solve this problem in your head. Two alien spaceships are traveling directly toward each other, one at 38,171 miles per hour, and the other at 21,829 miles per hour. They originated on planets 82,710,317 mile apart. How far apart will they be one minute before they collide?
HINT:
The distance between their home planets is irrelevant.
Answer:
1,000 miles...........The two spacecrat are approaching each other at a combined speed of 60,ooo mile per hour (38,171 + 21,829). This means the distance between them is closing at 1,000 miles per minute.
NO PENCIL--NO PAPER
Credit: Mike Androtti---Parade Magazine---Ask Marilyn by Marilyn Vos Savant
Solve this problem in your head. Two alien spaceships are traveling directly toward each other, one at 38,171 miles per hour, and the other at 21,829 miles per hour. They originated on planets 82,710,317 mile apart. How far apart will they be one minute before they collide?
HINT:
The distance between their home planets is irrelevant.
Answer:
1,000 miles...........The two spacecrat are approaching each other at a combined speed of 60,ooo mile per hour (38,171 + 21,829). This means the distance between them is closing at 1,000 miles per minute.
Monday, 26 April 2010
Sunday, 25 April 2010
DAY 232
LEFTOVERS AGAIN?
Credit: GAMES Magazine
June, 1984
Michael W. Ecker
What is the smallest whole number that, when divided by 2 leaves a remainder of 1; when divided by 3, leaves a remainder of 2; and so on, and when divided by 10 leaves a remainder of 9?
Answer:
2,519...............Since the remainder is always 1 less than the divisor, it follows that the answer must be 1 less than a multiple of all the divisors 2 through 10. The smallest such number must be the Least Common Multiple of 2, 3, 4, ...........9, 10 minus 1. The LCM is 2,520, so the answer is 2, 519.
LEFTOVERS AGAIN?
Credit: GAMES Magazine
June, 1984
Michael W. Ecker
What is the smallest whole number that, when divided by 2 leaves a remainder of 1; when divided by 3, leaves a remainder of 2; and so on, and when divided by 10 leaves a remainder of 9?
Answer:
2,519...............Since the remainder is always 1 less than the divisor, it follows that the answer must be 1 less than a multiple of all the divisors 2 through 10. The smallest such number must be the Least Common Multiple of 2, 3, 4, ...........9, 10 minus 1. The LCM is 2,520, so the answer is 2, 519.
Wednesday, 21 April 2010
Tuesday, 20 April 2010
DAY 230
SQUARE DANCE
Credit: GAMES Magazine - Oct/Nov 1987
Guney Mentes
Sally invited 17 guests to her party. She assigned each guest a number from 2 to 18, keeping 1 for herself. When everyone was dancing, Sally noticed that the sum of each couple's numbers was a perfect square. What was the number of Sally's partner?
HINT:
Start with guest 18.
Answer:
Sally's partner was guest 15. The pairings were 18-7, 17-8, 16-9, 15-1, 14-2, 13-3, 12-4, 11-5, and 10-6.
SQUARE DANCE
Credit: GAMES Magazine - Oct/Nov 1987
Guney Mentes
Sally invited 17 guests to her party. She assigned each guest a number from 2 to 18, keeping 1 for herself. When everyone was dancing, Sally noticed that the sum of each couple's numbers was a perfect square. What was the number of Sally's partner?
HINT:
Start with guest 18.
Answer:
Sally's partner was guest 15. The pairings were 18-7, 17-8, 16-9, 15-1, 14-2, 13-3, 12-4, 11-5, and 10-6.
Sunday, 4 April 2010
DAY 228
A man and woman 63 miles apart start traveling toward each other at the same time. If the man covers 4 miles per hour to the woman's 3 miles per hour, how far will each have traveled upon meeting?
Answer:
36 miles for the man and 27 miles for the woman...........They are approaching each other at 7 miles per hour, so they will meet in 9 hours.
A man and woman 63 miles apart start traveling toward each other at the same time. If the man covers 4 miles per hour to the woman's 3 miles per hour, how far will each have traveled upon meeting?
Answer:
36 miles for the man and 27 miles for the woman...........They are approaching each other at 7 miles per hour, so they will meet in 9 hours.
DAY 227
I can paint a room in 8 hours and you can do it in 10. How long would it take us working together?
Answer:
4 4/9 hours..........I can do 1/8 of the job in one hour and you can do 1/10 of the job in one hour. 1/8 + 1/10 = 9/40. Together we can do 9/40 of the job in one hour. 9/40 divided into 1 = 4 4/9.
I can paint a room in 8 hours and you can do it in 10. How long would it take us working together?
Answer:
4 4/9 hours..........I can do 1/8 of the job in one hour and you can do 1/10 of the job in one hour. 1/8 + 1/10 = 9/40. Together we can do 9/40 of the job in one hour. 9/40 divided into 1 = 4 4/9.
DAY 226
At the time of his marriage, a man found his wife's age to be 3/4 of his age. After 12 years of marriage, he found it to be 5/6 of his age. Find their ages at the time they were married.
Answer:
The man was 24 and his wife 18...........If X is the man's age at the time of their marriage, and 3/4 X the age of his wife, then after 12 years............(3/4 X + 12) = 5/6 (X + 12).
At the time of his marriage, a man found his wife's age to be 3/4 of his age. After 12 years of marriage, he found it to be 5/6 of his age. Find their ages at the time they were married.
Answer:
The man was 24 and his wife 18...........If X is the man's age at the time of their marriage, and 3/4 X the age of his wife, then after 12 years............(3/4 X + 12) = 5/6 (X + 12).
Saturday, 3 April 2010
DAY 223
You are going to run 12 miles and hope to do it at an average speed of 6 miles per hour. You are running uphill and when you arrive at the halfway point (the top of the hill) you realize you have averaged only 3 miles per hour. How fast must you run downhill to make the entire round trip's average speed 6 miles per hour.
Answer:
Sorry, unless you have a time machine, it's not going to happen. To run 12 miles at 6 miles per hour would take two hours. When you get to the top of the hill, you have run 6 miles. At an average speed of 3 miles per hour, this has taken you 2 hours. You have used up all your time and are only half-way through the run.
You are going to run 12 miles and hope to do it at an average speed of 6 miles per hour. You are running uphill and when you arrive at the halfway point (the top of the hill) you realize you have averaged only 3 miles per hour. How fast must you run downhill to make the entire round trip's average speed 6 miles per hour.
Answer:
Sorry, unless you have a time machine, it's not going to happen. To run 12 miles at 6 miles per hour would take two hours. When you get to the top of the hill, you have run 6 miles. At an average speed of 3 miles per hour, this has taken you 2 hours. You have used up all your time and are only half-way through the run.
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