A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Given:

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream than to return downstream to the same spot.

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$=x+18$ km/hr

Speed of the boat upstream$=18-x$ km/hr

Time taken by the boat to go 24 km downstream$=\frac{24}{x+18}$ hours

Time taken by the boat to go 24 km upstream$=\frac{24}{18-x}$ hours

Therefore,

$\frac{24}{18-x}-\frac{24}{x+18}=1$

$\frac{24(x+18)-24(18-x)}{(x+18)(18-x)}=1$

$\frac{24x+432-432+24x}{(18)^2-x^2}=1$

$\frac{48x}{324-x^2}=1$

$48x=1(324-x^2)$   (On cross multiplication)

$48x=324-x^2$

$x^2+48x-324=0$

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

$x^2+54x-6x-324=0$

$x(x+54)-6(x+54)=0$

$(x+54)(x-6)=0$

$x+54=0$ or $x-6=0$

$x=-54$ or $x=6$

Speed cannot be negative. Therefore, the value of $x$ is $6$ km/hr.

The speed of the stream is $6$ km/hr.

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Updated on: 10-Oct-2022

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