Question

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

Answer 1

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

speed of the boat in still water = 18 km/hr.
Total Distance = 24 km.

We know that,
Speed of the boat up stream = speed of the boat in still water − speed of the stream
= (18 − x) km/hr

Speed of the boat down stream = speed of the boat in still water + speed of the stream
= (18 + x) km/hr

Time of up stream journey = t₁ = $\frac{24}{18-x}$ hr

Time of down stream journey = t₂ = $\frac{24}{18+x}$ hr

According to the question,

t₁ − t₂ = 1 hr
$$\begin{gathered} \Rightarrow \frac{24}{18-x}-\frac{24}{18+x}=1 \\ \Rightarrow \frac{24(18+x-18+x)}{(18-x)(18+x)}=1 \\ \Rightarrow \frac{24\left(2x\right)}{(18{)}^2-x^2}=1 \\ \Rightarrow 48x=324-x^2 \\ \Rightarrow x^2+48x-324=0 \\ \Rightarrow x^2+54x-6x-324=0 \\ \Rightarrow x(x+54)-6(x+54)=0 \\ \Rightarrow (x-6)(x+54)=0 \\ \Rightarrow x-6=0\mathrm{or}x+54=0 \\ \Rightarrow x=6\mathrm{or}x=-54 \end{gathered}$$

Since, speed cannot be negative.

Thus, speed of the stream is 6 km/hr.