If 8 men can dig 16 holes in 32 days, how long will it take 1 man to dig 2 holes of the same size?
Answer:
32 days.............The ratios are the same.
Tuesday, 9 February 2010
DAY 217
Lucky you, your neighbor has seven pets. Some are dogs, the rest are cats. Each dog eats five biscuits and each cat eats four biscuits. 32 biscuits in all are eaten by the seven pets. How many are dogs and how many are cats?
Answer:
4 dogs, 3 cats...........Each animal eats at least 4 biscuits. So the seven pets eat the first 28 biscuits, leaving 4. These must go, one each, to the dogs, since they eat five biscuits each.
Lucky you, your neighbor has seven pets. Some are dogs, the rest are cats. Each dog eats five biscuits and each cat eats four biscuits. 32 biscuits in all are eaten by the seven pets. How many are dogs and how many are cats?
Answer:
4 dogs, 3 cats...........Each animal eats at least 4 biscuits. So the seven pets eat the first 28 biscuits, leaving 4. These must go, one each, to the dogs, since they eat five biscuits each.
Monday, 8 February 2010
DAY 215
A man walking a dog along a staraight road spots a friend in the distance. They wave to one another and the dog sprints ahead to greet her. As soon as it arrives, the dog turns around and runs straight back to the man. It then turns again and runs back to the woman, and continues doing this until the man and woman meet. If the man and woman are initially one mile apart, and each walks at a steady pace of 3 miles per hour, and the dog runs at 9 miles per hour, how far does the dog run?
Answer:
1 1/2 miles.............At a combined speed of 6 miles per hour, the man and woman meet in 10 minutes (1/6 hour). At a speed of 9 miles per hour, the dog would cover
a mile and one half (D = 9 x 1/6).
A man walking a dog along a staraight road spots a friend in the distance. They wave to one another and the dog sprints ahead to greet her. As soon as it arrives, the dog turns around and runs straight back to the man. It then turns again and runs back to the woman, and continues doing this until the man and woman meet. If the man and woman are initially one mile apart, and each walks at a steady pace of 3 miles per hour, and the dog runs at 9 miles per hour, how far does the dog run?
Answer:
1 1/2 miles.............At a combined speed of 6 miles per hour, the man and woman meet in 10 minutes (1/6 hour). At a speed of 9 miles per hour, the dog would cover
a mile and one half (D = 9 x 1/6).
Friday, 5 February 2010
DAY 214
Two watches are started at the same time. One runs two minutes per hour slow, and the other one minute per hour fast. How long must the watches run for the fast watch to be exactly one hour ahead of the slow watch?
Answer:
20 hours.........At the end of the first hour, the slow watch will have gone 58 minutes, while the fast watch will have gone 61 minutes. So every hour the fast watch gains 3 minutes on the slow one.
Two watches are started at the same time. One runs two minutes per hour slow, and the other one minute per hour fast. How long must the watches run for the fast watch to be exactly one hour ahead of the slow watch?
Answer:
20 hours.........At the end of the first hour, the slow watch will have gone 58 minutes, while the fast watch will have gone 61 minutes. So every hour the fast watch gains 3 minutes on the slow one.
Wednesday, 3 February 2010
DAY 212
How can you cook a pie for nine continuous minutes using two ungraduated egg-timers, one that runs for four minutes and one that runs for seven minutes?
Answer:
Put the pie in the oven and start both timers. When the first one runs out, turn it over. (Elapsed time so far is 4 minutes.) When the seven-minute timer runs out, turn it over too. When the first timer runs out again (after a total of 8 minutes), the seven-minute timer has been running for one minute since it was re-started. Turn it over again. When the one minute runs out, the pie is ready.
How can you cook a pie for nine continuous minutes using two ungraduated egg-timers, one that runs for four minutes and one that runs for seven minutes?
Answer:
Put the pie in the oven and start both timers. When the first one runs out, turn it over. (Elapsed time so far is 4 minutes.) When the seven-minute timer runs out, turn it over too. When the first timer runs out again (after a total of 8 minutes), the seven-minute timer has been running for one minute since it was re-started. Turn it over again. When the one minute runs out, the pie is ready.
Tuesday, 2 February 2010
DAY 210
Two boys and one girl can beat a man in a tug-of-war. A woman can beat one boy and two girls. Who would win in a contest between a man and one girl against a woman and one boy?
HINT:
Pit the two winning teams against the two losing teams.
Answer:
The mother and boy team will win. Boy + boy + girl + woman (the two winning teams combined) will defeat man + boy + girl + girl (the two losing teams combined). Subtract one boy and one girl from each side, and boy + woman deeats man + girl.
Two boys and one girl can beat a man in a tug-of-war. A woman can beat one boy and two girls. Who would win in a contest between a man and one girl against a woman and one boy?
HINT:
Pit the two winning teams against the two losing teams.
Answer:
The mother and boy team will win. Boy + boy + girl + woman (the two winning teams combined) will defeat man + boy + girl + girl (the two losing teams combined). Subtract one boy and one girl from each side, and boy + woman deeats man + girl.
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