Question

Question 7
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 40km downstream. Find the speed of the stream.

Answer 1

Let the speed of the stream be v km/h.
The speed of a person rowing in still water = 5 km/h
The speed of a person rowing downstream = (5 + v)km/h [His speed + speed of the stream]
And the speed of a person rowing upstream = ( 5 – v ) km/h [His speed - speed of the stream, as rowing upstream is in the direction opposite to that of the flow of the stream]
Now, time taken by the person to cover 40 km downstream is
$t_1=\frac{40}{5+v}h[\because speed=\frac{distance}{time}]$
and the time taken by the person to cover 40km upstream is
$t_2=\frac{40}{5-v}h$
By the given condition, $t_2=t_1\times 3$
$\Rightarrow \frac{40}{5-v}=\frac{40}{5+v}\times 3$
$\therefore v=\frac{10}{4}=2.5km/h$
Hence, the speed of the stream is 2.5 km/h.