Question

The ratio of the speeds of a boat in still water and the speed of the river is 3 ∶ 1. The boat takes 45 minutes for a round trip journey. Find the distance of the whole trip if the speed of the stream is 4 km/hr.
1. 4 km
2. 16 km
3. 8 km
4. 12 km

Answer 1

Correct Answer - Option 3 : 8 km

Given:

The speed of the boat in still water:  The speed of river = 3 : 1

Time is taken for the round trip = 45 mins

Speed of the stream = 4 km/h

Formula used:

Speed = Distance/Time

Upstream = Speed of the boat - speed of the river

Downstream = Speed of the boat + speed of the river

Average speed = (2xy)/(x + y)

where x and y are speed

Calculation:

Time in hours

45/60 = 3/4 hours

The speed of the river is 4 km/h

Then the speed of the boat will be 3 × 4 = 12 km/h

Upstream = 12 - 4 = 8 km/h

Downstream =  12 + 4 = 16 km/h

Average speed = ( 2 × 8 × 16)/(8 + 16)

⇒ 256/24 = 32/3 km/h

Distance = (32/3) × (3/4) = 8 km

∴ The distance of the whole trip is 8 km.