Question

A boat, which has a speed of $5\text{km/h}$ in still water, crosses a river of width $1\text{km}$ along the shortest possible path in $15$ minutes. The velocity of the river water in kilometers per hour is

• A. $1$
• B. $3$
• C. $4$
• D. $\sqrt{41}$

Answer 1

The correct option is B $3$

Let $V_r=$ Velocity of river
$V_b=$ Velocity of boat
$V_{br}=$ Velocity of boat w.r.t river
Velocity diagram for shortest path

Given $V_{br}=5\text{kmph}$
$t_{short}=15\text{min}=\frac{1}{4}hr$
$\text{width of river}=1\text{km}$
$t=\frac{\text{width}}{V_b}=\frac{1}{4}\Rightarrow V_b=4\text{kmph}$
Using pythagoras theorem
$\Rightarrow V_r=\sqrt{V_{br}^2-V_b^2}$
$V_r=\sqrt{25-16}=3\text{kmph}$