A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

To find the velocity of the river, we first calculate the resultant velocity of the boat. The boat covers a width of 1 km in 15 minutes. Since 15 minutes is 0.25 hours, the resultant velocity is 1 divided by 0.25, which equals 4 km per hour. For the shortest possible path, the boat moves perpendicular to the river flow. This creates a right-angled triangle where the speed in still water (5 km/hr) is the hypotenuse, the resultant velocity (4 km/hr) is one side, and the river velocity is the other side. According to the Pythagorean theorem, the square of the hypotenuse (25) equals the sum of the squares of the other two sides. Subtracting the square of the resultant velocity (16) from 25 gives 9. The square root of 9 is 3. Therefore, the river velocity is 3 km/hr.