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Wait - catch up problem

Problem Solving — algebra and arithmetic
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by wind612 » Sat Apr 23, 2011 9:21 pm
A hiker walking at a constant rate of 4m/h is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20m/h. The cyclist stops to wait for the hiker 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?
a. 6 2/3
b. 15
c. 20
d. 25
e. 26 2/3
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by jaymw » Sat Apr 23, 2011 11:54 pm
I assume you meant to write km/h instead of m/h.

When two items move in the same direction with different rates, we can subtract their individual rates to find out the distance between them

To calculate with the same units, consider that 5 minutes=1/12h

Now use the formula: Distance = Time*Rate

1/12h*(20-4)km/h=1/12h*16km/h=16/12km=4/3km

5 minutes after the cyclist passed the hiker, 4/3km lie between the cyclist and the hiker. Now the question is how long the hiker will need to cover this very distance given his rate of 4km/h

4/3km/4kmh=1/3h=20min

C is correct.
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