A motor boat whose speed in still water is 9 km/hr in still water, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

Given:

A motor boat whose speed in still water is 9 km/hr in still water, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes.

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$=x+9$ km/hr

Speed of the boat upstream$=9-x$ km/hr

Time taken by the boat to go 15 km downstream$=\frac{15}{x+9}$ hours

Time taken by the boat to go 15 km upstream$=\frac{15}{9-x}$ hours

$45$ minutes in hours$=\frac{45}{60}=\frac{3}{4}$

$3$ hours $45$ minutes $=3+\frac{3}{4}=\frac{4\times3+3}{4}=\frac{15}{4}$ hours

Therefore,

$\frac{15}{x+9}+\frac{15}{9-x}=\frac{15}{4}$

$\frac{15(9-x)+15(x+9)}{(x+9)(9-x)}=\frac{15}{4}$

$\frac{135-15x+15x+135}{(9)^2-x^2}=\frac{15}{4}$

$\frac{270}{81-x^2}=\frac{15}{4}$

$4(270)=15(81-x^2)$   (On cross multiplication)

$4(18)=81-x^2$

$x^2+72-81=0$

$x^2-9=0$

$x^2=9$

$x=3$

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

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Updated on: 10-Oct-2022

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