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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?
Answer: 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.
Solution:
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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.
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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.
If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?
Answer: Twenty one. Most people would think there were 42 handshakes. The first person shakes the hand of 6 others, the second person shakes the hand of 5 remaining people, the third person shakes the hand of 4 remaining people, the fourth person shakes the hand of 3 remaining people, the 5th person shakes the hand of 2 remaining people and the sixth person shakes the hand of 1 remaining person. 6+5+4+3+2+1=21
Solution:
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Twenty one. Most people would think there were 42 handshakes. The first person shakes the hand of 6 others, the second person shakes the hand of 5 remaining people, the third person shakes the hand of 4 remaining people, the fourth person shakes the hand of 3 remaining people, the 5th person shakes the hand of 2 remaining people and the sixth person shakes the hand of 1 remaining person. 6+5+4+3+2+1=21
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Twenty one. Most people would think there were 42 handshakes. The first person shakes the hand of 6 others, the second person shakes the hand of 5 remaining people, the third person shakes the hand of 4 remaining people, the fourth person shakes the hand of 3 remaining people, the 5th person shakes the hand of 2 remaining people and the sixth person shakes the hand of 1 remaining person. 6+5+4+3+2+1=21
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