A motorboat's speed in still water is 15 km/h. It goes 30 km downstream and returns in 4 h 30 min. What is the stream speed?

Given data

• Still-water speed v = 15 km/h; stream speed = s
• Downstream speed = 15 + s; upstream speed = 15 − s
• Total time T = 4.5 h

Concept / Approach

• Use time sum: 30/(15 + s) + 30/(15 − s) = 4.5.

Step-by-step calculation
30 ( 1 / ( 15 + 𝑠 ) ) + ( 1 / ( 15 − 𝑠 ) ) (1/(15+s))+(1/(15−s)) = 4.530 × ( 30 ) / ( 225 − 𝑠 2 ) (30)/(225−s 2 ) = 4.5 ⇒ 900/(225 − s^2) = 4.5900 = 4.5(225 − s^2) ⇒ 900 = 1012.5 − 4.5s^24.5s^2 = 112.5 ⇒ s^2 = 25 ⇒ s = 5 km/h

Verification
Downstream 30/(20) = 1.5 h; Upstream 30/10 = 3 h; total = 4.5 h ✔

Final Answer
5 km/h