Question

The speed of a boat in still water is $11\mathrm{km}/\mathrm{hr}$. It can go $12\mathrm{km}$ upstream and return downstream to the original point in $2$ hrs $45$ min. Find the speed of the stream.

Answer 1

Determining the speed of the stream

Let the speed of the stream be $x\mathrm{km}/\mathrm{hr}$ .

Given that the speed of the boat in still water is $11\mathrm{km}/\mathrm{hr}$.

Thus, the upstream speed of the boat will become $(11+x)\mathrm{km}/\mathrm{hr}$ and the downstream speed will become $(11-x)\mathrm{km}/\mathrm{hr}$.

The total time taken to go $12\mathrm{km}$ upstream and return to the original point downstream is $2$ hrs $45$ min, i.e. $165$ minutes.

As per the given condition,

$$\begin{gathered} \frac{12}{11+x}+\frac{12}{11-x}=\frac{165}{60} \\ \Rightarrow 12\left[\frac{11-x+11+x}{({11}^2-x^2)}\right]=\frac{11}{4} \\ \Rightarrow \frac{24}{121-x^2}=\frac{1}{4} \\ \Rightarrow 96=121-x^2 \\ \Rightarrow x^2=25 \\ \therefore x=\pm 5 \end{gathered}$$

Since the speed of the stream cannot be negative,

$\therefore x=5$

Therefore, the speed of the stream is $5\mathrm{km}/\mathrm{hr}$.