question_answer

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

Answer:

Let the speed of the stream be x km/hr.

Then speed upstream \[=(24-x)km/hr.\]

and speed downstream \[=(24+x)km/hr.\]

Time taken to cover 32 km upstream \[=\frac{32}{24-x}hrs.\]

Time taken to cover 32 km downstream \[=\frac{32}{24+x}hrs.\]

\[\therefore \] Time difference \[=\frac{32}{24-x}-\frac{32}{24+x}=1\]

\[32[(24+x)-(24-x)]=(24-x)(24+x)\]

\[32(24+x-24+x)=576-{{x}^{2}}\]

\[64x=576-{{x}^{2}}\]

\[{{x}^{2}}+64x-576=0\]

\[{{x}^{2}}+72x-8x-576=0\]

\[x(x+72)-8(x+72)=0\]

\[(x+72)(x-8)=0\]

\[x=8\] or \[-72\]

\[\therefore x=8\] (As speed can?t be negative)

\[\therefore \] Speed of the stream is \[8\,km/h.\]