Time to travel with the current: What time will a boat take to cover 128 km downstream if its still water speed is 24 km/h and the stream speed is 8 km/h?

Introduction / Context:Time taken for a journey equals distance divided by effective speed. For downstream travel, the effective speed is the still water speed plus the stream speed, because the current aids motion.

Given Data / Assumptions:

• Distance D = 128 km
• Still water speed u = 24 km/h
• Stream speed v = 8 km/h
• Uniform flow, straight course

Concept / Approach:Downstream speed sd = u + v. Time t = D / sd. Ensure units remain in km and h.

Step-by-Step Solution:

Verification / Alternative check:If the current were absent, time would be 128/24 ≈ 5.33 h. With a helping current, time must be shorter. The computed 4 h is consistent.

Why Other Options Are Wrong:

• 6 h, 7 h, and 8 h are longer than still-water time and contradict aid from current.
• 3 h would require a speed of about 42.7 km/h, which exceeds u + v = 32 km/h.

Common Pitfalls:Using average of u and v, or subtracting instead of adding for downstream. Always add the stream speed for downstream travel.

Final Answer:4 h