Question

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

Answer 1

let the river speed be Vr

speed of stream is3km/hr

Answer 2

Answer:

• Let thespeed of the stream = x km/hr

• Speed of motorboat = 9 km/hr

• Speed of downstream = 9 + x

• Speed of upstream = 9 - x

• Distance = 15 km

• Time taken to go upstream = 15/9-x

• Time taken to go downstream = 15/9+x

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$:\implies \sf \dfrac{15}{(9+x)} +\dfrac{15}{(9-x)}=\dfrac{15}{4}$

$:\implies \sf \dfrac{1}{(9+x)} +\dfrac{1}{(9-x)}=\dfrac{1}{4}$

$:\implies \sf \dfrac{9 \cancel{ - x} + 9 \cancel{+ x}}{(9+x)(9 - x)}=\dfrac{1}{4}$

$:\implies \sf\dfrac{18}{ {9}^{2} - {x}^{2} }=\dfrac{1}{4}$

$:\implies \sf\dfrac{18}{ 81 - {x}^{2} }=\dfrac{1}{4}$

$:\implies \sf 4( 18) = 1(81 - {x)}^{2}$

$:\implies \sf 72 = 81 - {x}^{2}$

$:\implies \sf {x}^{2} = 81 - 72$

$:\implies \sf {x}^{2} = 9$

$:\implies \underline{ \boxed{\textsf{ \textbf{ x = 3 km/hr}}}}$