A motor boat whose speed is 18km/h in still water takes 1 hour more to go 24km upstream then to return downstream to the same spot. Find the speed of the stream.
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Let the speed of the stream be x km/hr.
Speed of the boat upstream = Speed of boat in still water – Speed of the stream
∴ Speed of the boat upstream = ( 18 – x ) km/hr
Speed of the boat downstream = Speed of boat in still water + Speed of the stream
∴ Speed of the boat downstream = ( 18 + x ) km/hr
Time of upstream journey = Time for downstream journey + 1 hr.
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Let the speed of stream be x km / hr
For upstream = ( 18 - x ) km / hr
For downstream = ( 18 + x ) km / hr
A.T.Q.
24 / 18 - x - 24 / 18 + x = 1
48 x = 324 - x²
x² + 48 x - 324 = 0
( x + 54 ) ( x - 6 ) = 0
x = - 54 or x = 6
Since speed can't be negative .
Therefore , speed of the stream is 6 km / hr .
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