The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

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Solution

Let the speed of the stream be x km/hr.
Given, speed of the boat in still water = 8 km/hr
Therefore, speed in upstream = 8-x km/hr
Speed in downstream = 8+x km/hr
Now, time taken by boat to go 22 km downstream = $fraction numerator 22 over denominator 8 plus x end fraction k m divided by h r$
Time taken by boat to go 15 km upstream= $fraction numerator 15 over denominator 8 minus x end fraction k m divided by h r$
Total time taken by boat = 5 hrs
Total time taken = time taken in downstream + time taken in upstream.
Therefore,
$fraction numerator 22 over denominator 8 plus x end fraction plus fraction numerator 15 over denominator 8 minus x end fraction equals 5 rightwards double arrow fraction numerator 22 left parenthesis 8 minus x right parenthesis plus 15 left parenthesis 8 plus x right parenthesis over denominator left parenthesis 8 plus x right parenthesis left parenthesis 8 minus x right parenthesis end fraction equals 5 rightwards double arrow 176 minus 22 x plus 120 plus 15 x equals 5 left parenthesis 64 minus x squared right parenthesis rightwards double arrow 296 minus 7 x equals 320 minus 5 x squared rightwards double arrow 5 x squared minus 7 x minus 24 equals 0 rightwards double arrow 5 x squared minus 15 x plus 8 x minus 24 equals 0 rightwards double arrow 5 x left parenthesis x minus 3 right parenthesis plus 8 left parenthesis x minus 3 right parenthesis equals 0 rightwards double arrow left parenthesis 5 x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis equals 0 rightwards double arrow x equals fraction numerator negative 8 over denominator 5 end fraction space o r space 3$

Since speed can not be negative hence the speed of stream is 3 km/hr.

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