The downstream swimming rate of a woman is three times her upstream swimming rate. If she covers 12 km upstream in 2.5 hours, what distance (in km) will she cover in 5 hours downstream?

Introduction / Context:
This problem links upstream and downstream swimming speeds through a given ratio. You are told how far the woman swims upstream in a given time and how her downstream rate compares to this upstream rate. From this, you must compute her downstream speed and then the distance she can cover in a specified time.

Given Data / Assumptions:
- Downstream swimming rate is three times the upstream swimming rate. - Upstream distance covered = 12 km. - Time upstream = 2.5 hours. - Required: distance swum in 5 hours downstream. - Let u be the upstream speed (km/h). - Then downstream speed = 3u (km/h).

Concept / Approach:
First compute the upstream speed using speed = distance / time. Once upstream speed u is known, downstream speed is 3u by the given relationship. The distance she swims downstream in 5 hours is then simply speed * time. No need to separate still water and current speeds because the ratio is given directly between upstream and downstream speeds.

Step-by-Step Solution:
Step 1: Upstream speed u = distance / time = 12 / 2.5 km/h. Step 2: 12 / 2.5 = 12 / (5 / 2) = 12 * 2 / 5 = 24 / 5 = 4.8 km/h. Step 3: Downstream speed = 3u = 3 * 4.8 = 14.4 km/h. Step 4: Time spent swimming downstream = 5 hours. Step 5: Distance = speed * time = 14.4 * 5 km. Step 6: 14.4 * 5 = 72 km.

Verification / Alternative check:
Check that the upstream rate and downstream rate are consistent with the ratio. Upstream speed is 4.8 km/h. Downstream speed is 14.4 km/h. Ratio downstream : upstream = 14.4 : 4.8 = 3 : 1, exactly as stated. Therefore, the calculations are internally consistent and the 72 km distance in 5 hours downstream is correct.

Why Other Options Are Wrong:
- 36 km would correspond to a downstream speed of only 7.2 km/h, which is not three times 4.8. - 42 km, 56 km, and 60 km likewise imply downstream speeds that are not equal to 3 times the upstream speed of 4.8 km/h.

Common Pitfalls:
Some learners misinterpret three times as adding instead of multiplying, using u + 3 for the downstream speed instead of 3u. Others make mistakes in converting 2.5 hours or in dividing 12 by 2.5. Keeping a clear step for computing the initial upstream speed and using precise arithmetic avoids these errors.

Final Answer:
In 5 hours downstream, the woman will cover 72 km.