A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the downstream speed in km/hr?

Question: A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the downstream speed in km/hr?

Solution:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr

ATQ,
30/(15 + x) + 30/(15 - x) = 4(1/2)
Or, 900/(225 - x²) = 9/2
Or, 9x² = 225
Or, x² = 25
∴ x = 5 km/hr

∴ The downstream speed = (15 + 5) km/hr = 20 km/hr