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by f2001290 » Sun Jun 17, 2007 9:02 am
15. A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
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by gmatfan » Sun Jun 17, 2007 9:50 am
If the hiker is doing 4mph, then he is doing 1 mile per 15 minutes, and 1/3 of a mile in 5 minutes.

The cyclist is going 20mph, or 5 miles in 15 minutes, or 5/3 miles in 5 minutes.

When the cyclist passes the hiker, they are at the exact same spot. 5 minutes later when the cyclist stops, the cyclist has gone 5/3 mile and the hiker has gone 1/3 of a mile.

The distance between them is 5/3-1/3=4/3 miles.

At the hikers pace of 1/3 mile per 5 minutes, it will take him 20 minutes to catch up.
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