A boat takes 40 minutes less to travel 10 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 8 km/hr then the speed of the stream is

Let stream speed be s km/h. Downstream speed = 8 + s, upstream speed = 8 - s. Time downstream = 10/(8 + s), time upstream = 10/(8 - s). Given: 10/(8 - s) - 10/(8 + s) = 40/60 = 2/3 hours. Cross-multiplying: 30(8 + s) - 30(8 - s) = 2(64 - s²), giving 60s = 128 - 2s², or s² + 30s - 64 = 0. Solving: (s + 32)(s - 2) = 0, so s = 2 (positive root). Stream speed is 2 km/h.