Question

A boat moves with a speed of $5km/h$ relative to water in a river flowing with a speed of $3km/h$ and having a width of $1km$. The time taken in a round trip, when boat travel shortest distance is

• A. $5min$
• B. $60min$
• C. $20min$
• D. $30min$

Answer 1

The correct option is D $30min$

Boat will take minimum time for a round trip if it moves perpendicular to the flow of river.
Velocity of boat in the direction perpendicular to the river =$\sqrt{(5^2-3^2)}$= $4km/h$
∴ Time for trip to that side,$t=\frac{1}{4}=0.25hr$
To come back, again he takes $0.25hr$ to cross the river.
∴ Minimum time taken for a round trip = $0.5h=30min$