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.
The correct option is A $$360$$ km Let the speed of the stream be $$x$$ km/h. Given, speed of water $$= 3$$ km/h Therefore, downstream speed $$= (x + 3)$$ km/h and upstream speed $$=(x-3)$$ km/h Again, 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/h Therefore, downstream speed $$= 21 + 3 = 24$$ km/h So, distance between the two towns $$=$$ Downstream speed $$\times$$ Time taken in downstream