A motorboat travels 165 Kilometers in 5 hours going up stream. It travels 305 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current

Solution:

Given that,

A motorboat travels 165 Kilometers in 5 hours going up stream.

It travels 305 kilometers going downstream in the same amount of time

Therefore,

Upstream distance = 165 km

Upstream time = 5 hours

Thus upstream speed is 33 km per hour

Downstream distance = 305 km

Downstream time = 5 hours

Thus downstream speed is 61 km per hour

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 61 ---- eqn 1

u - v = 33 ----- eqn 2

Add eqn 1 and eqn 2

u + v + u - v = 61 + 33

2u = 94

u = 47

Substitute u = 47 in eqn 1

47 + v = 61

v = 61 - 47

v = 14

Thus rate of the boat in still water is 47 km/hr and rate of the current is 14 km/hr

15

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