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

Answer 1

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

$=24\times 15=360$ km