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.
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