A motor boat whose speed in still water is 18km/hr takes 1 hour more to g 24km up stream that to return down stream to the same spot. Find the speed of the stream.

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Solution

let the usual speed of stream be x km/hr,

Speed of the boat in still water is = 18 km/hr

Distance to be travelled = 24 km.

Speed of theboat upstream = speed of the boat in still water – speed of the stream = (18 – x) km/hr

Speed of the boat downstream = speed of the boat in still water + speed of the stream = (18 + x) km/hr.

Time of upstream journey, $t subscript 1 space equals space fraction numerator 24 over denominator 18 minus x end fraction$ km/hr

Time of downstream journey, $t subscript 2 equals fraction numerator 24 over denominator 18 plus x end fraction$ km/hr

Acc. To the question, = 1hr

$fraction numerator 24 over denominator 18 â�� x end fraction â�� fraction numerator 24 over denominator left parenthesis 18 plus x right parenthesis end fraction equals 1$
$fraction numerator 24 left parenthesis 18 plus x â�� 18 plus x over denominator left parenthesis 18 â�� x right parenthesis left parenthesis 18 plus x right parenthesis end fraction equals 1$
$fraction numerator 24 left parenthesis 2 x right parenthesis over denominator 18 squared â�� x squared end fraction equals 1$

Since the speed can never be negative

Therefore the speed of stream is 6 km/hr.

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