A boat takes 90 minutes less to travel 36 miles downstream than upstream. If its still-water speed is 10 mph, what is the stream speed?

Given data

• Distance each way = 36 miles
• Boat speed in still water = 10 mph; stream speed = s mph
• Upstream time − downstream time = 90 min = 1.5 h

Concept / Approach

• Use times: 36/(10 − s) − 36/(10 + s) = 1.5.

Step-by-step calculation36 1 10 − 𝑠 − 1 10 + 𝑠 10−s 1 ​ − 10+s 1 ​ = 1.536 × ( 10 + 𝑠 ) − ( 10 − 𝑠 ) 100 − 𝑠 2 100−s 2 (10+s)−(10−s) ​ = 1.536 × 2 𝑠 100 − 𝑠 2 100−s 2 2s ​ = 1.5 ⇒ \frac{72s}{100 − s^2} = 1.572s = 1.5(100 − s^2) ⇒ 1.5s^2 + 72s − 150 = 0Multiply by 2: 3s^2 + 144s − 300 = 0 ⇒ s^2 + 48s − 100 = 0Discriminant = 48^2 + 4×100 = 2704 = 52^2 ⇒ s = (−48 + 52)/2 = 2

Final Answer2 mph