Question

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

Please show each and every step.

Better type the answer than in a book. (:

Answer 1

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Answer 2

speed of motor boat = 18 kmph
speed of stream = x

speed of motor boat in upstream = 18 + X
speed of motor boat in downstream = 18 - x

time taken to cover the same distance in downstream = t
then, time taken to cover the same distance in upstream = t + 1
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$\frac{24}{18 + x} = t$
$\frac{24}{18 - x} = t + 1 \\ \frac{24}{18 - x} - 1 = t$

equalising t = t
then,
$\frac{24}{18 + x} = \frac{24}{18 - x} + 1 \\ \frac{24}{18 + x} - \frac{24}{18 - x} = + 1 \\ \frac{24(18 - x) - 24(18 + x)}{ {18}^{2} - {x}^{2} } = +1 \\432 +24x - 432 +24x = +{18}^{2} - {x}^{2} \\ 48x = 324 - {x}^{2} \\ {x}^{2} + 48x - 324 = 0 \\ {x}^{2} + 54x - 6x - 324 = 0\\ x(x + 54) - 6(x - 54) = 0 \\ (x-6)(x-54) = 0 \\ x = 6 kmph / X = 54 kmph$
as, speed of motor boat is always greater than the speed of stream so, the speed of stream will be 6 kmph.