Question

A boat takes $10$ hours to travel $30$ km upstream and $44$ km downstream, but it takes $13$ hours to travel $40$ km upstream and $55$ km downstream. Find the speed of the boat in still water and the speed of the stream.

Answer 1

Let the speed of the boat in still water be $u$ and speed of the stream be $v$.

The speed while going upstream is $u-v$ and going downstream is $u+v$.

We know that $Time=\frac{Distance}{Speed}$, hence we write the following equations:

$\frac{30}{u-v}+\frac{44}{u+v}=10$

$\frac{40}{u-v}+\frac{55}{u+v}=13$

Let $u-v=x$ and $u+v=y$, the equations become,

$\frac{30}{x}+\frac{44}{y}=10$ ........ $\left(1\right)$

$\frac{40}{x}+\frac{55}{y}=13$ ........ $\left(2\right)$

Using $3\times equation\left(2\right)-4\times equation\left(1\right),$ we get:

$\frac{165}{y}-\frac{176}{y}=39-40$

We get $y=11$.

Substituting the value in (1), we get $x=5$. Hence $u+v=11$ and $u-v=5$.

Therefore, speed of the boat in still water $u=8km/h$ and speed of the stream is $v=3km/h$.