Q. A boat takes two hours to travel 8 km and back in still water. If the velocity of water 4 $kmh^{- 1}$, the time taken for going ups tream 8km and coming back is

A) 2h
B) 2 h 40 min
C) 1 h 20 min
D) Cannot be estimated with the information given
Explanation

(b) Boat covers distance of 16 km in a still water in hours
$ie\ \ v_{B} = \frac{16}{2} =$8$kmh^{- 1}$
Now, velocity of water
$v_{W} = 4kmh^{- 1}$
Time taken for going upstream
$t_{1} = \frac{8}{v_{B} - v_{w}} = \frac{8}{8 - 4} = 2$h
(As water current oppose the motion of boat) Time taken for going downstream
$t_{2} = \frac{8}{v_{B} + v_{w}} = \frac{8}{8 + 4} = \frac{8}{12}$h
(As water current helps the motion of boat)
$\therefore$ Total time $= t_{1} + t_{2}$
$= \left( 2 + \frac{8}{12} \right)$h=2 h 40 min

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.