A swimmer desires to cross a 500 m wide river that is flowing at 5 km/h . His speed relative to the water is 3 km/h . Determine the shortest possible time in minutes to cross the river.

Step-by-step solution

Let the width of the river be d = 500 m = 0.5 km . The velocity of the swimmer relative to the water is v_ s = 3 km/h . The velocity of the river flow is v_ r = 5 km/h . To cross the river in the shortest possible time, the swimmer must head exactly perpendicular to the river flow. The component of the swimmer's velocity along the width of the river is maximum in this case and is equal to v_ s . The shortest time taken to cross the river is given by: t_ min = d v_ s t_ min = 0.5 3 hours Converting the time into min