A motorboat can travel at 5 km/hr in still water. It travelled 45 km downstream in a river and then returned, taking altogether 50 hours. Find the rate of flow of the river.

Question: A motorboat can travel at 5 km/hr in still water. It travelled 45 km downstream in a river and then returned, taking altogether 50 hours. Find the rate of flow of the river.

Solution:
Speed of boat in still water, x = 5 km/hr.
Let,
rate of flow of river = y km/hr.
∴ Speed of upstream = 5 - y
speed of downstream = 5 + y

∴ 45/(5 + y) + 45/(5 - y) = 50
⇒ (225 - 45y + 225 + 45y)/(25 - y²) = 50
⇒ 450 = 1250 - 50y²
⇒ 50y² = 800
⇒ y² = 16
∴ y = 4 km/hr.