Question

A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is 4 km/h. Find the distance between the two towns.

Answer 1

Let velocity of the streamer be $V_s$

Let distance between the 2 towns be $d$

Velocity of water = 4 km/h

$\therefore$, velocity of streamer downstream = $V_s+4$

Velocity of the streamer upstream = $V_s-4$

Velocity downstream$=V_s+4=\frac{d}{20}\left(1\right)$

Velocity upstream$=V_s-4=\frac{d}{25}\left(2\right)$

Subtracting $\left(2\right)$ from $\left(1\right)$, we get

$8=\frac{d}{20}-\frac{d}{25}\Rightarrow 8=\frac{d}{5}(\frac{1}{4}-\frac{1}{5})\Rightarrow 40=\frac{d}{20}\Rightarrow d=800km$

Hence, distance between the 2 towns = 800 km.