Ravi's speed of rowing in still water is 6 km/hr. He rows between two points in a river and return to the same starting point. He took 30 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 2
The correct answer is Option (2) → 2.25 km
Given:
Speed of Ravi in still water: $u = 6$ km/hr
Speed of stream: $v = 3$ km/hr
Time difference upstream and downstream: $\Delta t = 0.5$ hours
Speed downstream: $u+v = 6+3 = 9$ km/hr
Speed upstream: $u-v = 6-3 = 3$ km/hr
Let distance between points be $d$ km.
Time downstream: $t_d = \frac{d}{9}$
Time upstream: $t_u = \frac{d}{3}$
Given $t_u - t_d = 0.5$
$\frac{d}{3} - \frac{d}{9} = 0.5$
$\frac{3d - d}{9} = 0.5 \Rightarrow \frac{2d}{9} = 0.5$
$2d = 4.5 \Rightarrow d = 2.25$ km