 # 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. 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.

Solution:

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 $=\frac{\text { distance covered }}{\text { Speed }}$

Total speed of the boat while going upstream $=15-x \mathrm{~km} / \mathrm{h}$

Time taken to go upstream $=\frac{30}{15-x}$ hrs

Total speed of boat while going downstream $=15+x \mathrm{~km} / \mathrm{h}$

Time taken to go upstream $=\frac{30}{15-x} \mathrm{hrs}$

Total speed of boat while going downstream $=15+x \mathrm{~km} / \mathrm{h}$

Time taken to go downstream $=\frac{30}{15+x}$ hrs

Total time of the journey $=4 \frac{1}{2} \mathrm{hrs}=4.5 \mathrm{hrs}$

$\Rightarrow \frac{30}{15-x}+\frac{30}{15+x}=4.5$

$\Rightarrow \frac{30[(15+x)+(15-x)]}{(15)^{2}-x^{2}}=4.5$

$\Rightarrow 30[15+x+15-x]=4.5\left[(15)^{2}-x^{2}\right]$

$\Rightarrow 30=4.5\left[225-x^{2}\right]$

$\Rightarrow \frac{30 \times 30}{4.5}=225-x^{2}$

$\Rightarrow 225-x^{2}=200$

$\Rightarrow x^{2}=25$

$\Rightarrow x=\pm 5$

Ignore the negative value.
So, the speed of the stream = x = 5 km/h