Question

# A steamer going downstream in a river, covers the distance between $$2$$ towns in $$15$$ hours. Coming back upstream, it covers this distance in $$20$$ hours. The speed of the water is $$3$$ km/hr. Find the distance between two towns.

A
360 km
B
220 km
C
180 km
D
120 km

Solution

## The correct option is A $$360$$ kmLet the speed of the stream be $$x$$ km/h.Given, speed of water $$= 3$$ km/h Therefore, downstream speed $$= (x + 3)$$ km/hand upstream speed $$=(x-3)$$ km/hAgain, time taken in downstream and upstream is $$15$$ hours and $$20$$ hours respectively.Now, distance downstream $$=$$ distance upstream$$\Rightarrow 15(x+3)=20(x-3)$$$$\Rightarrow 15x+45=20x-60$$$$\Rightarrow 15x-20x=-60-45$$$$\Rightarrow -5x=-105$$ or $$x=21$$ km/hTherefore, downstream speed $$= 21 + 3 = 24$$ km/hSo, distance between the two towns $$=$$ Downstream speed $$\times$$ Time taken in downstream $$= 24 \times 15 = 360$$ kmPhysics

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