Correct Answer - Option 4 : 4.5 h
Given:
A boat travels a certain distance upstream at 18 km/hr and the same distance downstream at 36 km/hr.
Formula:
Upstream = (u − v) km/hr
Downstream = (u + v) km/hr
where “u” is the speed of the boat in still water and “v” is the speed of the stream
Speed of Boat in Still Water = 1/2 (Downstream Speed + Upstream Speed)
Speed of Stream = 1/2 (Downstream Speed – Upstream Speed)
Calculation:
Speed of the stream = 1/2 (Downstream Speed – Upstream Speed)
Speed of the stream = 1/2 (36 - 18) = 9 km/hr
Speed of Boat in Still Water = 1/2 (Downstream Speed + Upstream Speed)
⇒ 1/2(36 + 18) = 27
Time to travel 54 km = {54/(27 - 9)} + {54/(27 + 9)}
⇒ (54/18) + (54/36) = 3 + 1.5 = 4.5
∴ The required time is 4.5 h.
