On a path, 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 & waits for the hiker 5 min 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
A. 6 2/3
B. 15
C. 20
D. 25
E. 26 2/3
Hiker's speed is 4m/hr
Cyclist's speed is 20 m/hr
They're both are moving in the same direction. If they were going the same speed and the same direction, each would appear like they were standing still to the other. So we need to think of how much faster the cyclist is--that's his effective rate from the perspective of the hiker. The effective speed of the cyclist is 20-4 which is 16 m/hr
So with this speed, the cyclist will travel 16/60 * 5 miles in 5 mins which is 4/3 miles
Back to D = rt. The Hiker will take (4/3)/4 hr to travel 4/3 miles at the speed of 4m/hr
So, the time required by the hiker is 1/3 hr = 20 mins
C
1 comment:
Rate Time Distance questions are really interesting to solve especially problems related to the same directions. I personally enjoy solving these questions. I am definitely gonna use this method because I found it very easy and short. Before this, I was using a long and difficult method.
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