 # A person,rowing at the rate of 5 km/h in still water,

Question:

A person,rowing at the rate of 5 km/h in still water,takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of

the stream.

Solution:

Let the speed of the stream be v km/h.

Given that, a person rowing in still water = 5 km/h

The speed of a person rowing in downstream = (5+ v) km/h

and the speed of a person has rowing in upstream = (5 – v) km/h

Now, the person taken time to cover 40 km downstream,

$t_{1}=\frac{40}{5+v} \mathrm{~h} \quad\left[\because\right.$ speed $\left.=\frac{\text { distance }}{\text { time }}\right]$

and the person has taken time to cover $40 \mathrm{~km}$ upstream,

$t_{2}=\frac{40}{5-v} h$

By condition, $t_{2}=t_{1} \times 3$

$\Rightarrow$ $\frac{40}{5-v}=\frac{40}{5+v} \times 3$

$\Rightarrow$ $\frac{1}{5-v}=\frac{3}{5+v}$

$\Rightarrow$ $5+v=15-3 v \Rightarrow 4 v=10$

$\therefore$ $v=\frac{10}{4}=2.5 \mathrm{~km} / \mathrm{h}$

Hence, the speed of the stream is 2.5 km/h,