Question

A boat is in a river where the speed of the stream is 15 km/hour. The boat travelled a distance of 50 km upstream and downstream in 3.5 hours. Find the time the boat will take to travel 90 km upstream and downstream when the speed of the stream is 25 km/hour.
1. 12.5
2. 10.5
3. 11.5
4. 11

Answer 1

Correct Answer - Option 2 : 10.5

Given:

A boat is in a river where the speed of the stream is 15 km/hour. The boat traveled a distance of 50 km upstream and downstream in 3.5 hours. 

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:

Let the speed of the boat in still water be u km/h

50/(u - 15) + 50/(u + 15) = 3.5

⇒ u = 35

⇒ Time = {90/(35 + 25)} + {90/(35 - 25)} = 1.5 + 9 = 10.5

∴ The boat will take 10.5 hours.