Question

A motor boat has a speed of 18 $\frac{km}{hr}$ in still water. It takes 2 hours and 45 minutes more to go 66 km upstream than to return downstream to the same spot. Find the speed of the stream in $km/hr.$

• A. $4km/hr$
• B. $5km/hr$
• C. $6km/hr$
• D. $7km/hr$

Answer 1

The correct option is C $6km/hr$

Let the speed of the stream be '$x$' and the time required to travel upstream be '$t$'.

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

Speed of boat in upstream
= Speed of boat - Speed of stream
= 18 - $x$

and, speed of boat in downstream
= speed of boat + speed of stream
= 18 + $x$

$\therefore$ From the given data,

$t=\frac{66}{(18+x)}$---------------(1)

$t+(2+\frac{3}{4})=\frac{66}{(18-x)}$

$t+\frac{11}{4}=\frac{66}{(18-x)}$------------(2)

Subtracting (1) from (2), we get

$\frac{11}{4}=66[\frac{1}{18-x}-\frac{1}{18+x}]$

$\Rightarrow 1=24\left[\frac{2x}{({18}^2-x^2)}\right]$

$\Rightarrow {18}^2-x^2=48x$

$\Rightarrow x^2+48x-{18}^2=0$

Now, the equation $x^2+48x-{18}^2=0$ can also be written as:

$x^2+2\left(24\right)x+{24}^2-{24}^2-{18}^2=0$

$\Rightarrow$$(x+24{)}^2-900=0$

$\Rightarrow$$(x+24{)}^2-{30}^2$= 0

$\Rightarrow$$(x+24{)}^2={30}^2$

$\Rightarrow$$x+24=\pm 30$ (Taking square root on both sides)

$\Rightarrow$ $x=-54$ or $x=6$

The speed of the stream cannot be negative.

So, the speed of the stream $=6km/hr$