A pilot of steamer is going in downstream with certain speed. Suddenly he saw some people at the bank of river and turns steamer to 90° towards them. After 2 hours of journey he reached at bank of river but was at distance of 8 km from them. The shortest distance between the point of turning in the river to point of reaching at bank of river is 17 km. Find the downstream speed with which boat was moving earlier.?

Option 1 : 11.5 km/hr

Given

Initially boat was moving in downstream

Distance between point of turning to point of reaching = 17 km

Distance between people to point of reaching = 8 km

Calculation

Point of turning, people and point of reaching makes a right angled triangle with hypotenuse = 17 km, one side = 8 km

⇒ Other side = √(17² – 8²) = √225 = 15 km

Boat is moving along hypotenuse and reached 8 km far from people in two hour river speed takes boat to 8 km in 2 hours

⇒ River speed = 8/2 = 4 km/hr

Boat was moving in vertical to river and distance was 15 km which was travelled in 2 hours

⇒ Speed of boat = 15/2 = 7.5 km/hr

Previously boat was moving in the direction of river

⇒ Downstream Speed = boat + river’s speed

⇒ Downstream Speed = 4 + 7.5 = 11.5 km/hr