Question

A motorboat whose speed is 18 kmph in still water takes 1 hr 30 min more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Let speed of stream be x km/h.

Given:

Speed of boat = 18 km/h
Distance covered upstream = 36 km
Distance covered downstream = 36 km
It takes $\frac{3}{2}\mathrm{hours}$ more to go 36 km upstream than to return downstream to the same spot

Now, Speed of boat upstream = 18 − x km/h
Speed of boat downstream = 18 + x km/h

$\frac{\mathrm{Distance}}{\mathrm{Speed}}=\mathrm{Time}$

According to the question,

Time to go upstream = $\frac{3}{2}$ hours + Time to go downstream

Time to go upstream − Time to go downstream = $\frac{3}{2}$

$$\begin{gathered} \frac{36}{18-x}-\frac{36}{18+x}=\frac{3}{2} \\ \Rightarrow \frac{36\left(18+x\right)-36\left(18-x\right)}{\left(18+x\right)\left(18-x\right)}=\frac{3}{2} \\ \Rightarrow \frac{648+36x-648+36x}{324-x^2}=\frac{3}{2} \\ \Rightarrow \frac{72x}{324-x^2}=\frac{3}{2} \\ \Rightarrow \frac{24x}{324-x^2}=\frac{1}{2} \\ \Rightarrow 24x\left(2\right)=324-x^2 \\ \Rightarrow x^2+48x-324=0 \\ \Rightarrow x^2+54x-6x-324=0 \\ \Rightarrow x\left(x+54\right)-6\left(x+54\right)=0 \\ \Rightarrow \left(x+54\right)\left(x-6\right)=0 \\ \Rightarrow x=-54,6 \\ \mathrm{But}x\mathrm{is}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{stream}\mathrm{which}\mathrm{is}\mathrm{always}\mathrm{positive}. \\ \mathrm{Thus},x=6\mathrm{km}/\mathrm{h} \end{gathered}$$


Hence, the speed of the stream is 6 km/h.