A motorboat can travel at 10 km/h in still water. It travelled 91 km downstream in a river and then returned to the same place, talking altogether 20 h. The rate of flow of river is?

Given, speed of boat = 10 km/h
Let speed of flow of river = x km/h
∴ Upstream speed of boat = (10 - x) km/h
and downstream speed of boat = = (10 + x) km/h
According to question.
91/(10 - x) + 91/(10 + x) = 20
⇒ 91(10 + x + 10 - x) / (10 - x) (10 + x) = 20
⇒ 91(20) / 100 - x² = 20
⇒ 91 = 100 - x²
⇒ x² = 9
∴ x = 3