Hey the answer is 20. Even I thought its 25 but after seeing your answer I got the logic.
Cyclist's speed is 20 miles/60 mins which is 1/3 miles per minute
Hiker's speed is 4 miles/60 mins which is 1/15 miles per minute
In 5 mins Cyclist would go 5/3 miles
In the same 5 mins hiker would go 1/3 miles.
So the cyclist has to wait for the hiker until he covers 5/3 minus 1/3 miles which is 4/3 miles. With a speed of 1/15 mile per minute the hiker would cover the distance 4/3 in 20 minutes.
Please correct me if I am wrong.
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time, distance, velocity q
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Stuart@KaplanGMAT
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There are two variations of this question:
First, we have two objects that are travelling in opposite (i.e. directly towards each other or directly away from each other). If we want to calculate relative velocities, we ADD their individual speeds.
Second, we have two objects travelling in the same direction (usually a catch-up question, like the one you posted). If we want to calculate relative velocities, we SUBTRACT one speed from the other.
So, in this example, the cyclist gains (20) - (4) = 16mph
5 minutes is 1/12th of an hour, so in the 5 minutes of travel the cyclist travels an extra 1/12(16) = 16/12 = 4/3 of a mile.
At a rate of 4mph, it takes (4/3)/(4) hours (4/3)(1/4) = 1/3 of an hour (or 20 minutes) to catch up.
First, we have two objects that are travelling in opposite (i.e. directly towards each other or directly away from each other). If we want to calculate relative velocities, we ADD their individual speeds.
Second, we have two objects travelling in the same direction (usually a catch-up question, like the one you posted). If we want to calculate relative velocities, we SUBTRACT one speed from the other.
So, in this example, the cyclist gains (20) - (4) = 16mph
5 minutes is 1/12th of an hour, so in the 5 minutes of travel the cyclist travels an extra 1/12(16) = 16/12 = 4/3 of a mile.
At a rate of 4mph, it takes (4/3)/(4) hours (4/3)(1/4) = 1/3 of an hour (or 20 minutes) to catch up.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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