Question

A boat can move in still water with 5 km/h, in 1 km wide river. A boat cross the l km wide river along shortest
path in 15 min. Find velocity of river in km/hr?​

Answer 1

Answer:

the boat travels with a velocity of 3 km/ h

Answer 2

Answer:

The river's velocity is 0.75 km/hr.

Explanation:

Boat speed = 5 km/hr

River width = AB = 1 km

Time taken by the boat to cross the river = 15 minutes = 1/4 hr

$\text {Velocity}=\frac{\text {Change in distance}}{\text {Time}}$

$\Rightarrow 5=\frac{\text {Change in distance}}{1 / 4}$

The change in distance by boat in 15 minutes = 1.25 km

Now,

The shortest distance is taken as AC = 1.25 km

$\angle \mathrm{B}=90^{\circ}$

Apply Pythagoras theorem in $\Delta \mathrm{ABC}$

$(\mathrm{AB})^{2}+(\mathrm{BC})^{2}=(\mathrm{AC})^{2}$

$\mathrm{BC}=\mathrm{0.75} \ \mathrm{km}$

So, the distance covered by the river water in 15 minutes is 0.75 km.

$\text{Velocity of the river} =0.75 /(1 / 4)=3 \ \mathrm{km} / \mathrm{hr}$