A man swims 72 km downstream in 9 hours and 45 km upstream in 9 hours. What is the speed of the current (in km/h)?

Introduction / Context:
This swimming problem is another boats and streams style question. You are given downstream and upstream journeys over different distances but equal times. From these journeys you can determine downstream and upstream speeds and then compute the speed of the current itself.

Given Data / Assumptions:
- Downstream distance = 72 km, time = 9 hours. - Upstream distance = 45 km, time = 9 hours. - Let b be the swimmer speed in still water (km/h). - Let c be the speed of the current (km/h). - Downstream speed = b + c, upstream speed = b - c.

Concept / Approach:
Compute the effective speeds in both directions by dividing distance by time. These are equal to b + c and b - c respectively. Once we have these values, adding and subtracting the two equations allows us to solve for b and c. The question specifically asks for the value of c, the current speed.

Step-by-Step Solution:
Step 1: Downstream speed = 72 / 9 = 8 km/h. Step 2: Upstream speed = 45 / 9 = 5 km/h. Step 3: So b + c = 8 and b - c = 5. Step 4: Add the equations: (b + c) + (b - c) = 8 + 5 gives 2b = 13. Step 5: Thus b = 13 / 2 = 6.5 km/h. Step 6: Substitute into b + c = 8: 6.5 + c = 8, so c = 8 - 6.5 = 1.5 km/h.

Verification / Alternative check:
Check the downstream and upstream speeds using b = 6.5 and c = 1.5. Downstream speed = 6.5 + 1.5 = 8 km/h, so time for 72 km is 72 / 8 = 9 hours, as given. Upstream speed = 6.5 - 1.5 = 5 km/h, so time for 45 km is 45 / 5 = 9 hours, also matching the question. Therefore, the current speed 1.5 km/h is correct.

Why Other Options Are Wrong:
- 1 km/h or 2 km/h would give different downstream and upstream speeds that do not match 8 km/h and 5 km/h. - 3.2 km/h and 2.5 km/h would cause large mismatches in times when checked back with the given distances.

Common Pitfalls:
Sometimes learners average the distances or the times instead of calculating speeds separately. Another error is mixing up downstream and upstream formulas. Always start with speed = distance / time, then identify which speed corresponds to b + c and which corresponds to b - c, and finally solve for c.

Final Answer:
The speed of the current is 1.5 km/h.