• # question_answer 31) 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.

 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 $8\,km/h.$