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  • A motorboat whose speed in still water is 9 km/h, 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.  

A motorboat whose speed in still water is 9 km/h, 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.

 

Answers (1)

Assume that time for downstream is = T

                                Time for upstream = t

T + t = 3 hours 45 mins = \frac{15}{4}hrs

                            T = \frac{15}{V + \nu}

                            T = \frac{15}{9 + \nu}\quad-(i)

        Similarly,

                            \frac{15}{9-\nu} = t - \quad - (ii)

[Where, V = speed of the boat and \nu = speed of stream]

Add eq (i) and (ii)           

\Rightarrow \frac{15}{(9 + \nu)} + \frac{15}{9 -\nu} = T + t

\Rightarrow \frac{15\times 18}{81 - \nu^2} = \frac{15}{4}

\Rightarrow \nu^2 = 81 - (18\times 4)

\Rightarrow \nu^2 = 9

\Rightarrow Speed of stream is 3 km/hr                 

Posted by

Safeer PP

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