Witchiegrlie wrote:

A hiker walking at a constant rate of 4 miles per hour was passed by a cyclist traveling at a rate of 20 miles per hour on the same path and in the same direction. The cyclist stops to wait for the hiker 5 minutes after passing him, while the hiker continues to walk at his constant rate. How many minutes must the cyclist wait until the hiker catches up?

1) 6 2/3

2) 15

3) 20

4) 25

5) 26 2/3

Speed of Hiker = 4 miles per hour = (1/15) miles per min

Speed of Cyclist = 20 miles per hour = (1/3) miles per min

Now Cyclist stops after 5 minutes ride.

That means he travelled for 5 minutes before he stopped.

So Distance covered by the cyclist = Speed * Time

= 1/3 * 5 = (5/3) miles

But Hiker has also walked for those 5 minutes so he must have covered the distance = (1/15) * 5 = (1/3)

Therefore, remaining distance to be covered by Hiker = 5/3 - 1/3 = 4/3
We need to find, how much time Hiker will take to cover 4/3 miles

Time = D/S = (4/3)/(1/15) = 20 minutes

And time taken by Hiker to travel (4/3) miles is equal to the time for which Cyclist should wait.

Hence C.

Good question.....

- Brajesh