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?
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.
