A motorboat, whose speed in 20 km/h in still water goes 40 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is-

Question: A motorboat, whose speed in 20 km/h in still water goes 40 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is-

Solution:
Let, the speed of the stream = x km/h
Then,
Speed downstream = (20 + x) km/h
Speed upstream = (20 - x) km/h

ATQ,
40/(20 + x) + 40/(20 - x) = 4.5
⇒ 1600/(400 - x²) = 9/2
⇒ 9(400 - x²) = 2 × 1600
⇒ 3600 - 3200 = 9x²
⇒ (3x)² = 20²
⇒ 3x = 20
⇒ x = 20/3
∴ x = 6.67

∴ The speed of the stream is 6.67 km/h