Question

The speed of a boat in still water is$11km/hr$. It can go $12km$ upstream and return downstream to its original point in $2hr45min$. Find out the speed of the stream.

Answer 1

Step1: Assumption of the speed of the stream, upstream and downstream

Let the speed of the stream $=xkm/hr$

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

Speed of the boat downstream $=(11+x)Km/hr$

Speed of the boat upstream $=(11–x)Km/hr$

Step2: Forming the equation according to the question.

$\begin{array}{rcl}\frac{12}{11-x}+\frac{12}{11+x}& =& 2\frac{45}{60}\end{array}$

Step3: Now solve the equation according to the question.

$\begin{array}{rcl}\frac{12(11+x)+12(11-x)}{\left(11-x\right)\left(11+x\right)}& =& 2\frac{3}{4}\\ \frac{132+\cancel{12x}+132-\cancel{12x}}{\left(11-x\right)\left(11+x\right)}& =& \frac{11}{4}\\ 264\times 4& =& 11(121-x^2)\\ (121-x^2)& =& 24\times 4\\ x^2& =& 121-96\\ x^2& =& 25\\ x& =& 5\end{array}$

The speed of the stream is $5Km/hr$.