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 for 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
Rate and time are RECIPROCALS.grandh01 wrote: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?
The RATE RATIO = hiker : cyclist = 4:20 = 1:5.
Thus, the TIME RATIO = hiker : cyclist = 5:1.
The implication is that the hiker will take 5 TIMES AS LONG as the cyclist to travel the same distance.
Thus, the hiker will need 25 minutes to travel the distance traveled by the cyclist in 5 minutes.
Thus, the cyclist will have to wait 20 minutes for the hiker to catch up.
