A swimmer whose speed in still water is 6 km/hr, swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1.5 km
Let the distance be d km. The stream adds to his speed downstream and reduces it upstream:
\(\text{Downstream speed} = 6 + 3 = 9 \text{ km/hr}\)
\(\text{Upstream speed} = 6 - 3 = 3 \text{ km/hr}\)
The upstream time exceeds the downstream time by 20 minutes, which is 1/3 hour:
\( \displaystyle \frac{d}{3} - \frac{d}{9} = \frac{1}{3} \)
\( \displaystyle \frac{2d}{9} = \frac{1}{3} \)
\(2d = 3,\quad d = 1.5\)
So the two points are 1.5 km apart.