A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.75 km
The speed in the pool is the speed in still water. The stream adds to it downstream and subtracts from it upstream:
\(\text{Downstream speed} = 5 + 2 = 7 \text{ km/h}\)
\(\text{Upstream speed} = 5 - 2 = 3 \text{ km/h}\)
Let the distance be d km. The upstream trip takes 20 minutes = \(\frac{1}{3}\) hour longer:
\( \displaystyle \frac{d}{3} - \frac{d}{7} = \frac{1}{3} \)
\( \displaystyle \frac{4d}{21} = \frac{1}{3} \)
\( \displaystyle d = \frac{21}{12} = \frac{7}{4} = 1.75 \)
So the two points are 1.75 km apart.