Question

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 1

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 = $\frac{32}{24-x}-\frac{32}{24+x}=1$

$32\left[\right(24+x)-(24-x\left)\right]=(24-x)(24+x)$

$32(24+x-24+x)=576-x^2$

$64x=576-x^2$

$x^2+64x-576=0$

$x^2+72x-8x-576=0$

$x(x+72)-8(x+72)=0$

$(x+72)(x-8)=0$

$x=8$ or $-72$

$\therefore x=8$

(As speed can't be negative)

$\therefore$ Speed of the stream is 8 km/h.