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
GivenSwimmer speed in still water: $u = 5$ km/h
Speed of stream: $v = 2$ km/h
Time difference: $\Delta t = 20$ min $= \frac{1}{3}$ h
Distance between points: $d$ km
Speed downstream: $u+v = 5+2 = 7$ km/h
Speed upstream: $u-v = 5-2 = 3$ km/h
Time downstream: $t_1 = \frac{d}{7}$ h
Time upstream: $t_2 = \frac{d}{3}$ h
Given $t_2 - t_1 = \frac{1}{3}$:
$\frac{d}{3} - \frac{d}{7} = \frac{1}{3}$
$\frac{7d - 3d}{21} = \frac{1}{3}$
$\frac{4d}{21} = \frac{1}{3} \Rightarrow 4d = 7 \Rightarrow d = \frac{7}{4} = 1.75$ km