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. The speed of the stream is ----- km/hr.

Answer 1

$\Rightarrow$ Let $x$ be the speed of the stream.

$\Rightarrow$ Speed of the boat in still water is $8km/hr$

$\Rightarrow$ The speed of the boat in upstream is $8-xkm/hr$

$\Rightarrow$ The speed of the boat in downstream is $8+xkm/hr$

$\Rightarrow$ The time taken by the boat to cover $15km=\frac{15}{8-x}hr$

$\Rightarrow$ The time taken by the boat to cover $22km=\frac{22}{8+x}hr$

According to the question,

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

$\Rightarrow$ $15(8+x)+22(8-x)=5(8-x)(8+x)$

$\Rightarrow$ $120+15x+176-22x=5(64-x^2)$

$\Rightarrow$ $296-7x=320-5x^2$

$\Rightarrow$ $5x^2-7x-24=0$

$\Rightarrow$ $5x^2-15x+8x-24=0$

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

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

$\Rightarrow$ $x-3=0$ and $5x+8=0$

$\Rightarrow$ $x=3$ and $x=-\frac{8}{5}$

Speed cannot be negative.

$\therefore$ The speed of the stream is $3km/hr$