Question

The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. [CBSE 2017]

Answer 1

Let, speed of stream be x km/h
Speed of boat = 15 km/h
Distance from each side = 30 km
We know that time taken $=\frac{\mathrm{distance}\mathrm{covered}}{\mathrm{Speed}}$
Total speed of the boat while going upstream $=15-x$ km/h
Time taken to go upstream $=\frac{30}{15-x}$ hrs
Total speed of boat while going downstream $=15+x$ km/h
Time taken to go downstream $=\frac{30}{15+x}$ hrs
Total time of the journey $=4\frac{1}{2}$hrs = 4.5 hrs
$$\begin{gathered} \Rightarrow \frac{30}{15-x}+\frac{30}{15+x}=4.5 \\ \Rightarrow \frac{30\left[(15+x)+(15-x)\right]}{(15{)}^2-x^2}=4.5 \\ \Rightarrow 30\left[15+x+15-x\right]=4.5\left[(15{)}^2-x^2\right] \\ \Rightarrow 30\left[30\right]=4.5\left[225-x^2\right] \\ \Rightarrow \frac{30\times 30}{4.5}=225-x^2 \\ \Rightarrow 225-x^2=200 \\ \Rightarrow x^2=25 \\ \Rightarrow x=\pm 5 \end{gathered}$$
Ignore the negative value.
So, the speed of the stream = x = 5 km/h