Question

The speed of a boat in still water is $11km/hr$. It can go $12km$ upstream and return to the original points in $2$ hours $45$ min. Find the speed of the stream.

Answer 1

Let the speed of the stream be $skm/hr$.

Speed of boat in still water $=11km/hr$

Speed of boat in upstream $=(11-s)km/hr$

Speed of boat in downstream $=(11+s)km/hr$

Distance $=12km$

Therefore $\frac{12}{11-s}+\frac{12}{11+s}=2\frac{3}{4}hr$

$\Rightarrow \frac{12(11+s+11-s)}{(11-s)(11+s)}=\frac{11}{4}$

$\Rightarrow \frac{12\times 22}{121-s^2}=\frac{11}{4}$

$\Rightarrow \frac{12\times 2}{121-s^2}=\frac{1}{4}$

$\Rightarrow 96=121-s^2$

$\Rightarrow s^2=25$

$\Rightarrow s=\pm 5$

Since speed cannot be negative, we take $s=5$
Therefore Speed of stream is $5km/hr$