Question

A boat takes 3.0 hours to travel $30\text{km}$down a river, then 5.0 hours to return. How fast is the river flowing?

Short answer

The speed of the river is $2\text{km}/\text{h}$.

Step-by-step solution

Step 1. Given information

The boat takes$3.0\text{h}$to travel $30\text{km}$ down a river, and it takes$5.0\text{h}$ to cover the same distance in return.

Step 2. Explanation

The speed of the boat is during the downstream is, $v+u=\frac{D}{t}$

Here, v is the speed of the boat, u is the speed of the stream, D is the total distance, and t is the time of row.

$\begin{array}{l}v+u=\frac{30\text{km}}{3.0\text{h}}\\ v=10.0\text{km}/\text{h}-u\end{array}$

The speed of the boat during upstream is,

$v-u=\frac{D}{t}$

$\begin{array}{l}(10.0\text{km}/\text{h}-u)-u=\frac{30\text{km}}{5.0\text{h}}\\ 2u=10.0\text{km}/\text{h}-6.0\text{km}/\text{h}\\ u=\frac{4.0\text{km}/\text{h}}{2}\\ =2.0\text{km}/\text{h}\end{array}$

Therefore, the speed of the river is $2\text{km}/\text{h}$.