Question

a motor ship covers the distance of 300 km between two localities on a river in 10 hrs downstream and in 12 hrs upstream the flow velocity of the river is n km/hr then the value of 2 n will be

Answer 1

Let the velocity of flow in the river be x kmph and the speed of the motor ship be s kmph.

While going downstream the ship takes 300/(s+x) = 10 hours, or

s + x = 30 …(1)

While going upstream the ship takes 300/(s-x) = 12 hours, or

s - x = 25 …(2)

Add (1) and (2)

2s = 55, or

s = 27.5 kmph and x = 30–27.5 = 2.5 kmph.

Check: While going downstream, time taken = 300/(27.5+2.5) = 300/30 = 10 hours. Correct.

While going upstream, time taken = 300/(27.5-2.5) = 300/25 = 12 hours. Correct.

The velocity of flow of the river is 2.5 kmph and the speed of the motor ship is 27.5 kmph, in still water.