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A boat travels 10 km upstream in 40 minutes and 15 km downstream in 30 minutes. Find the time taken by the boat to cover a distance of 45 km in still water.


1. 1 minute
2. 2 hours
3. 60 seconds
4. 1.5 hours
5. 45 minutes

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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.

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