A river flows at 5 km/h. A swimmer can swim at 20 km/h in still water. He swims 30 km downstream from point A to point B, then immediately turns and swims 30 km upstream back to A. What is the total time taken?

Introduction / Context:When speeds are given for still water and the current, the effective downstream and upstream speeds are v + c and v − c, respectively. For fixed distances on each leg, compute times separately and add them.

Given Data / Assumptions:

• Still water speed v = 20 km/h.
• Current speed c = 5 km/h.
• Downstream and upstream distances both equal 30 km.

Concept / Approach:Downstream speed = 25 km/h; upstream speed = 15 km/h. Time = distance / speed for each leg. Sum the two times for total duration.

Step-by-Step Solution:

Verification / Alternative check:Compute in minutes: 1.2 h = 72 min; add 120 min = 192 min = 3 h 12 min, consistent.

Why Other Options Are Wrong:2 h 30 min and 3 h 30 min or 3 h 45 min are not equal to 192 min under the given speeds.

Common Pitfalls:Using an average of 25 and 15 over the full 60 km; averages of speeds do not apply to mixed legs with different effective speeds.

Final Answer:3 h 12 min