# A boat has a speed of 5 km/hr in still water.It crosses a river of width 1 km along the shortest possible path in 15 min. What is the velocity of the river water.

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The boat has a speed of 5 km/h in still water. It crosses a river that is 1 km wide along the shortest possible path in 15 minutes.

Let the speed at which the water in the river is flowing be V. And the angle of the boat to the line along the shore against the direction of the flowing water be A.

The speed of the boat has two components 5*sin A opposite to the direction of the flowing water and 5*cos A perpendicular to the shore. If the boat crosses the river along the shortest path, 5*sin A = V. The river is crossed in 15 minutes. This gives 5*cos A = 4

=> cos A = 4/5

`sin A = sqrt(1 - (4/5)^2) = 3/5`

`V = 5*(3/5) = 3`

**The speed at which the water in the river is flowing is 3 km/h**