Correct Answer - Option 2 : 2 hours
Given:
Distance covered by boat in upstream = 10 km
Time taken by boat in upstream = 40 minutes
Distance covered by boat in downstream = 15 km
Time taken by boat in downstream = 30 minutes
Distance covered by boat in still water = 45 km
Formula used:
Speed of boat in still water = (Upstream speed + Downstream speed)/2
Speed = (Distance/Time)
Upstream speed = (Speed of boat) - (Speed of current)
Downstream speed = (Speed of boat) + (Speed of current)
Calculation:
Let the speed of boat in still water be x km/h.
and speed of current be y km/h
Time taken by boat in upstream = 40 minutes
⇒ (40/60) hour
⇒ (2/3) hour
Upstream speed = [10/(2/3)]
⇒ (x - y) = (10/2) × 3
⇒ (x - y) = 15 km/h ----(1)
Time taken by boat in downstream = 30 minutes
⇒ (30/60) hour
⇒ (1/2) hour
Downstream speed = [15/(1/2)]
⇒ (x + y) = 30 km/h ----(2)
Now, add equation (1) and equation (2)
(x - y) + (x + y) = 15 + 30
⇒ 2x = 45
⇒ x = 22.5
Speed of boat in still water = 22.5 km/h
Time taken by boat to cover a distance of 45 km in still water = [45/(22.5)]
⇒ 2 hours
∴ Time taken by boat to cover a distance of 45 km in still water will be 2 hours.
