Question

A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is

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

Answer 1

Answer: (B)

2h 40 min

Answer 2

Boat covers distance of 16km in a still water in 2 hours.

i.e. $v_{B} = \frac{16}{2} = 8km/hr$

Now velocity of water $\Rightarrow v_{w} = 4km/hr$

Time taken for going upstream

$t_{1} = \frac{8}{v_{B} - v_{w}} = \frac{8}{8 - 4} = 2hr$

(As water current oppose the motion of boat)

Time taken for going down stream

$t_{2} = \frac{8}{v_{B} + v_{w}} = \frac{8}{8 + 4} = \frac{8}{12}hr$

(As water current helps the motion of boat)

$\therefore$ Total time $= t_{1} + t_{2} = \left( 2 + \frac{8}{12} \right)hr$ or 2hr 40min