Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well.
If you can run ten miles per hour, how fast is the train moving?
The train is moving at 40 miles per hour. Imagine that a friend is walking with you. When the train whistle blows, you head away from the train, he heads toward it. When he reaches safety, you will be 6/8 (or 3/4)of the way across the bridge, and the train will have just reached the bridge. For the train to cross 4/4 of the bridge in the time you cross the remaining 1/4, the train must be moving four times your speed.
John was very tired after a long day of work. He went to bed at 10 p.m., wound his alarm clock and set it for noon the next day. Since John fell asleep almost immediately, how many hours of sleep did he get before the alarm woke him?
Two hours. Wind-up clocks can't be set more than 12 hours in advance.
Three cars had driven into a parking lot at the same time, and the three drivers left them all for the
attendant to park. Unfortunately, he isn't too good at remembering exactly which driver drove which car.
However, he is sure of these 6 facts:
a. Colin drove the BMW if and only if Mr. Cooper drove the Avenger.
b. Alan drove the Cortina if and only if Mr. Cooper drove the BMW.
c. Colin is Mr. Brown if and only if Mr. Andrews drove the BMW.
d. Brian is Mr. Andrews if and only if Colin drove the BMW.
e. Mr. Cooper drove the Avenger if and only if Alan is Mr. Brown.
f. Colin is Mr. Brown if and only if Alan drove the Cortina.
Who arrived with which car?
Brian Brown drove the BMW, Alan Andrew's drove the Avenger,
and Colin Cooper drove the Cortina.
An officer wishing to arrange his men in a solid square found by his first arrangement that he had 39 men left over. He then started increasing the number of men on a side by one, but found that 50 additional men would be needed to complete a new square. How many men did the officer have?
The officer had 1975 men. When he formed a square measuring 44 by 44, he had 39 men over. When he tried to form a square 45 x 45, he was 50 men short.