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Logic Puzzle
By Ben Allan on Tuesday, April 02, 2002 - 09:08 pm:

I have a logic puzzle:

A green car and a red car are 100 miles away from each other.The green car travels at 80 miles an hour. the red car travels at 20 miles an hour. There is a bird above the green car that flies towards the red car until it meets it, then goes back to the green car and so on.
The bird travels at 50 miles an hour.

How far will the bird have traveled when the cars collide?

By Kondwani Kanjere on Wednesday, April 03, 2002 - 08:50 pm:

Assuming that both cars are going in the same direction, taking this as the positive direction, and that the green car is following the red car.

The speed of the green car with respect to the red car = +60mph
so the time taken for the two cars to collide will be = (100/60)hrs (since time = distance/speed)
In this time the bird would have flown a distance of = (100)/60)×(50) (since distance = speed × time)
= 83.33 miles (4 sgf)

By Ben Allan on Thursday, April 04, 2002 - 11:50 am:

Sorry as the cars are going towards each other

By Jasjot Singh Kohli on Saturday, April 06, 2002 - 02:59 am:

100 miles

By Chris Tynan on Saturday, April 13, 2002 - 09:42 am:

If the cars are going towards each other, they will collide once they have covered a distance of 100 miles between them. This occurs after one hour, since the red car has travelled twenty miles and the green car 80.
So, the bird will have travelled 50 miles in the hour before the cars collide

By Ben Allan on Saturday, April 13, 2002 - 03:48 pm:

Very good Chris!

By The Editor

For a famous story about von Neumann solving this problem, see http://www.primepuzzle.com/leeslightest/howfar.html