A boat's still-water speed is 9 km/h and the stream speed is 1.5 km/h. For a 105 km trip downstream and return upstream, what is the total time?

Given data

• u = 9 km/h, v = 1.5 km/h
• Distance each way = 105 km

Concept / Approach

• Downstream speed = u + v; upstream speed = u − v.
• Total time = distance/downstream speed + distance/upstream speed.

Step-by-step calculation

Downstream speed = 9 + 1.5 = 10.5 km/h ⇒ time = 105/10.5 = 10 hUpstream speed = 9 − 1.5 = 7.5 km/h ⇒ time = 105/7.5 = 14 hTotal time = 10 + 14 = 24 hours

Verification

Check: 10.5 × 10 = 105; 7.5 × 14 = 105.

Common pitfalls

• Using average of speeds for round trips; harmonic-like addition is required via time sum.

Final Answer

24 hours