A boat covers a distance of 338 km upstream in 13 hours. After rain, the speed of the stream increases by 50%, and the speed of the boat in still water decreases by 25% due to low visibility. Following this, the boat takes 7 hours to travel 294 km downstream. Determine the difference between the speed of the boat in still water after the rain and the speed of the stream after the rain.

ATQ, Let the speed of boat in still water before rain be x km/h. And, the speed of stream before rain be y km/h. So, the upstream speed before rain = (x – y) = 338 ÷ 13 x – y = 26 ------(i) Speed of boat in still water after rain = 0.75x km/h Speed of stream after rain = 1.5 y km/h Downstream speed of boat after rain = 0.75x + 1.5y = 294 ÷ 7 0.75x + 1.5y = 42 -------(ii) On solving (i) and (ii), we get x = 36 km/h and y = 10 km/h So, the speed of boat in still water after rain = 0.75 × 36 = 27 km/h Speed of stream after rain = 1.5 × 10 = 15 km/h Required difference = 27 – 15 = 12 km/h