# The speed of a boat in still water is 8 km/hr.

Question:

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Solution:

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

Speed downstream $=(8+x) \mathrm{km} / \mathrm{hr}$.

Therefore, Speed upstream $=(8-x) \mathrm{km} / \mathrm{hr}$

Time taken by the boat to go $15 \mathrm{~km}$ upstream $=\frac{15}{(8-x)} \mathrm{hr}$

Time taken by the boat to returns $22 \mathrm{~km}$ downstream $=\frac{22}{(8+x)} \mathrm{hr}$

Now it is given that the boat returns to the same point in 5 hr.

So,

$\frac{15}{(8-x)}+\frac{22}{(8+x)}=5$

$\frac{15(8+x)+22(8-x)}{(8-x)(8+x)}=5$

$\frac{120+15 x+176-22 x}{64-x^{2}}=5$

$\frac{296-7 x}{64-x^{2}}=5$

$5 x^{2}-7 x+296-320=0$

$5 x^{2}-7 x-24=0$

$5 x^{2}-15 x+8 x-24=0$

$5 x(x-3)+8(x-3)=0$

$(x-3)(5 x+8)=0$

$x=3, x=-\frac{8}{5}$

But, the speed of the stream can never be negative.

Hence, the speed of the stream is $x=3 \mathrm{~km} / \mathrm{hr}$