Finding still water speed from unequal travel times: A boat covers 48 km downstream in 20 h and the same 48 km upstream in 24 h (4 h more). What is the speed of the boat in still water?

Introduction / Context:
When downstream and upstream times for the same distance are known, we can compute the corresponding speeds and then infer the still water speed as the average of the two effective speeds. This uses the linear nature of relative motion with current.

Given Data / Assumptions:

• Distance each way = 48 km
• Downstream time = 20 h
• Upstream time = 24 h
• Uniform current

Concept / Approach:
Downstream speed sd = distance / time. Upstream speed su = distance / time. Still water speed u = (sd + su) / 2. Current speed v = (sd - su) / 2 (not required but useful for checks).

Step-by-Step Solution:

Verification / Alternative check:
Then v = (2.4 - 2.0) / 2 = 0.2 km/h. Check: downstream u + v = 2.2 + 0.2 = 2.4 matches sd, and upstream u - v = 2.0 matches su.

Why Other Options Are Wrong:

• 2.0 km/h and 4.0 km/h are one of the effective speeds or unrelated.
• 4.2 km/h and 1.8 km/h do not satisfy the downstream and upstream pair with the given times.

Common Pitfalls:
Using arithmetic mean of times or distances incorrectly. Here we average effective speeds, not times. Keep units consistent.

Final Answer:
2.2 km/h