a motorboat whose speed in still water is 18 km per hour takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream.
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24/18-x - 24/18+x = 1
324-x^2 = 48x
x^2 +48x-324= 0
x^2+54x - 6x -324=0
(x^2+54x)-(6x+324)=0
x(x+54)-6(x+54)=0
x=6 kmph
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Answer:
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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