A boat covers 84 km downstream in 4 hours. It takes the same time to cover 42 km downstream as to cover 30 km upstream. How much time (in hours) will the boat take to travel 45 km upstream?

Solution

Let speed of boat in still water = b km/h, speed of stream = s km/h. From first condition: Downstream speed = b + s 84 km in 4 hours ⇒ b + s = 84/4 = 21 km/h …(1) From second condition: Time for 42 km downstream = time for 30 km upstream: 42 / (b + s) = 30 / (b − s) Use (1): b + s = 21 ⇒ 42 / 21 = 30 / (b − s) 2 = 30 / (b − s) b − s = 15 km/h …(2) Now solve (1) and (2): b + s = 21 b − s = 15 Add: 2b = 36 → b = 18 km/h Then s = 21 − 18 = 3 km/h Upstream speed = b − s = 15 km/h Time for 45 km upstream = 45 / 15 = 3 hours.