Question

A motor boat whose speed is 18 $\frac{km}{hr}$ in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.​

• A. 4
• B. 5
• C. 6
• D. -54

Answer 1

The correct option is C

6

Let the speed of the stream is ‘x’. Let the time required to travel downstream be ‘t’.

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

t= $\frac{24}{(18+x)}$---------------(1)

t+1 = $\frac{24}{(18-x)}$------------(2)

Subtracting equation 1 from equation 2, we get

$\Rightarrow$1=24$[\frac{1}{18-x}-\frac{1}{18+x}]$

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

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

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

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

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

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

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

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

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

The speed of the stream cannot be negative

Therefore, the speed of the stream = 6 km/hr