A boat can cross a river by following two different strategies. The ratio of the time taken to cross the river along the shortest possible path to the minimum possible time to cross the river is 5 4 . If the boat drifts by 120 m when it crosses the river in the minimum possible time, the width of the river is :

Step-by-step solution

Let v_b be the speed of the boat in still water, v_r be the speed of the river flow, and d be the width of the river. The minimum time to cross the river is when the boat is steered perpendicular to the river flow: t_ min = d v_b The time taken to cross along the shortest path (zero drift) is: t_ short = d v_b^2 - v_r^2 Given that the ratio of these times is 5 4 : t_ short t_ min = v_b v_b^2 - v_r^2 = 5 4 Squaring both sides: v_b^2 v_b^2 - v_r^2 = 25 16 16v_b^2 = 25v_b^2 - 25v_r^2 9v_b^2 = 25v_r^2 v_r v_b = 3 5 Whe