## Wednesday, August 02, 2006

### Run faster!

In a 10 kilometer race, Alex beat Bob by 20 meters and Carl by 40 meters. If Bob and Carl were to run a 10 kilometer race, and Bob gave Carl a 20-meter head start, who would probably win?

1. Alex! Because that fast little bastard would start racing the both of them 10 meters into the race!

2. Bob would win (assuming everyone runs at approximately constant velocity). If the distance between Bob and Carl was 20 meters when Alex finished the race, that means that Bob had gained 20 meters on Carl when Carl had run 9.96 kilometers. In the second scenario, Bob will have 9.98 kilometers of Carl-running to catch him, which should be more than enough time to do so and pass him for the win (but just barely).

3. While Alex would win if he was running ;-), I have to agree with Abe.

Bob will win.

When the two of them ran against Alex, Bob was exactly 20 meters ahead of Carl at the moment Alex crossed the finish line. With a 20 meter head start, they will be even at that point, i.e. 20 meters from the finish line. Bob is the faster runner, so in that last 20 meters, he should beat Carl since he's the faster runner.

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