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
Speed of swimmer in still water $=6$ km/hr
Speed of stream $=3$ km/hr
Speed downstream $=6+3=9$ km/hr
Speed upstream $=6-3=3$ km/hr
Let distance between the two points be $d$ km
Time downstream $=\frac{d}{9}$ hr
Time upstream $=\frac{d}{3}$ hr
Given upstream time exceeds downstream time by $20$ minutes $=\frac{1}{3}$ hr
$\frac{d}{3}-\frac{d}{9}=\frac{1}{3}$
$\frac{3d-d}{9}=\frac{1}{3}$
$\frac{2d}{9}=\frac{1}{3}$
$2d=3$
$d=\frac{3}{2}$
The distance between the two points is $\frac{3}{2}$ km.