## Thursday, January 31, 2008

### Get a Little Exercise Today

Bill and Judy set out to cover a certain distance by foot. Bill walks half the distance and runs half the distance. Judy walks half the time and runs half the time. Bill and Judy walk and run at the same rate. Who will reach the finish line first?

1. I'm going to leave this up for another day since the blog seems to be down for some reason. Arggghhh... bad blogger, bad!

2. Judy. Assuming they run faster than they walk, walking half the distance will take longer than half of the time- thus, you cover more distance in half the time running that running half the distance.

3. If they run and walk at the same speed, then it will be a tie. But otherwise, the one who walks half the time and runs half the time (Judy) will win.

Example: Suppose they are traveling 20 miles and they walk at 4 miles per hour and run at 5 miles per hour. Then Bill's equations (runs half the distance and runs half the distance) will look like this:
4t = 10 miles => t = 2.5 hours
5t = 10 miles => t = 2 hours
Total time = 4.5 hours

Judy's equations look like this:
4(1/2 t) + 6(1/2 t) = 2t + 3t = 20 => t = 4 hours.

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