Question

A motorboat whose speed in still water is $18km/h$, takes $1hour$ more to go $24km$ upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Given that, the speed of the motorboat in still water is $18km/h$

Let's consider the speed of the stream $=s$

Speed of boat upstream $=$ Speed of a boat in still water $-$ the speed of a stream

Speed of boat upstream $=18-s$

Speed of boat downstream $=$ Speed of a boat in still water $+$ speed of a stream

Speed of boat downstream $=18+s$

Time is taken for upstream $=$ Time taken to cover downstream $+$ $1$

Since, $time=\frac{dis\tan ce}{speed}$

So, $\frac{Dis\tan c{e}_{upstream}}{Spee{d}_{upstream}}=\frac{Dis\tan c{e}_{downstream}}{Spee{d}_{downstream}}+1$

$$\begin{gathered} \Rightarrow 24/(18–s)=[24/(18+s\left)\right]+1 \\ \Rightarrow 24(18+s)=24(18-s)+(18-s)(18+s) \\ \Rightarrow s^2+48s-324=0 \\ \Rightarrow s^2+54s-6s-324=0 \\ \Rightarrow (s+54)(s-6)=0 \\ \Rightarrow s=6or-54 \end{gathered}$$

But,$s\ne -54$ since the speed of steam cannot be negative.

∴ The speed of the stream is $6km/hr$.