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.

Given:

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.

To do:

We have to find the speed of the stream.

 Solution:

Let the speed of the stream be $x$ km/hr.

This implies,

Speed of the boat downstream$=x+8$ km/hr

Speed of the boat upstream$=8-x$ km/hr

Time taken by the boat to go 22 km downstream$=\frac{22}{x+8}$ hours

Time taken by the boat to go 15 km upstream$=\frac{15}{8-x}$ hours

Therefore,

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

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

$\frac{176-22x+15x+120}{(8)^2-x^2}=5$

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

$-7x+296=5(64-x^2)$   (On cross multiplication)

$-7x+296=320-5x^2$

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

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

Solving for $x$ by factorization method, we get,

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

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

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

$5x+8=0$ or $x-3=0$

$5x=-8$ or $x=3$

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

Speed cannot be negative. Therefore, the value of $x$ is $3$ km/hr.

The speed of the stream is $3$ km/hr.

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Updated on: 10-Oct-2022

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