A motorboat covers 48 km downstream and 30 km upstream

Solution

ATQ, Let downstream speed = D km/h, upstream speed = U km/h. From the data: 48/D + 30/U = 6 …(1) 64/D + 20/U = 6 …(2) Let 1/D = x and 1/U = y. Then: 48x + 30y = 6 …(1') 64x + 20y = 6 …(2') Subtract (1') from (2'): (64 − 48)x + (20 − 30)y = 0 16x − 10y = 0 ⇒ 16x = 10y ⇒ y = (16/10)x = (8/5)x. Substitute y into (1'): 48x + 30 × (8/5)x = 6 48x + 48x = 6 96x = 6 x = 6/96 = 1/16. So, D = 1/x = 16 km/h. Now y = (8/5)x = (8/5) × (1/16) = 8/80 = 1/10 ⇒ U = 10 km/h. Speed of boat in still water, B = (D + U)/2 = (16 + 10)/2 = 13 km/h. Speed of stream, S = (D − U)/2 = (16 − 10)/2 = 3 km/h. Answer: Boat speed = 13 km/h; stream speed = 3 km/h.