A motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

Explanation

Speed of the motorboat in still water = 24 km/hr.
Let the speed of the stream be x km/hr.
Then, speed upstream `=(24-x)km/hr.`
Speed downstream `=(24-x)km/hr.`
Time taken to go 32 km upstream `=(32)/((24-x))` hours.
Time taken to return 32 km downstream `=(32)/((24+x))` hours.
`:." "(32)/((24-x))-(32)/((24+x))=1`
`implies" "(1)/((24-x))-(1)/((24+x))=(1)/(32)implies((24+x)-(24-x))/((24-x)(24+x))=(1)/(32)`
`implies" "(2x)/((576-x^(2))=(1)/(32)implies576-x^(2)=64x`
`implies" "x^(2)+64x-576=0impliesx^(2)+72x-8x-576=0`
`implies" "x(x+72)-8(x+72)=0implies(x+72)(x-8)=0`
`implies" "x+72=0" or "x-8=0`
`implies" "x=-72" or "x=8`
`implies" "x=8" "[because" speed of the stream cannot be negative"]`
Hence, the speed of the stream is 8 km/hr.