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
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.