A woman’s downstream swimming speed is three times her upstream swimming speed. If she covers 12 km upstream in 2.5 hours, how much distance (in km) will she cover in 5 hours downstream?

Introduction / Context:
This swimming problem describes a relationship between upstream and downstream speeds. The downstream speed is three times the upstream speed, and we are given the upstream distance and time. From this, we can compute the upstream speed, derive the downstream speed, and then calculate how far the woman can swim downstream in a given time. It illustrates proportional reasoning in the context of relative motion in water.

Given Data / Assumptions:

• Upstream distance = 12 km.
• Upstream time = 2.5 hours.
• Downstream speed = 3 times upstream speed.
• We need downstream distance in 5 hours.
• Speeds are constant, and water flow is uniform.

Concept / Approach:
First we compute upstream speed from distance and time. Then downstream speed is given as three times that upstream speed. Once downstream speed is known, we simply multiply it by the given downstream time to find the required distance. This problem does not require separate still water and stream speeds; it only needs the effective speeds.

Step-by-Step Solution:
Upstream distance = 12 km, upstream time = 2.5 hours. Upstream speed = distance / time = 12 / 2.5 km/h. Compute 12 / 2.5 = 4.8 km/h. Given that downstream speed = 3 times upstream speed. So downstream speed = 3 * 4.8 = 14.4 km/h. Time available downstream = 5 hours. Downstream distance = speed * time = 14.4 * 5 = 72 km.

Verification / Alternative check:
We can double check the calculations. Upstream speed of 4.8 km/h over 2.5 hours gives 4.8 * 2.5 = 12 km, which matches the given upstream distance. Downstream speed of 14.4 km/h for 5 hours yields 14.4 * 5 = 72 km, which is consistent with the proportional relation provided. The internal arithmetic is straightforward and fully supports the answer.

Why Other Options Are Wrong:
If we mistakenly used a different multiple or computed upstream speed incorrectly, we might get values like 36 km, 56 km, or 42 km. However, those values do not match a downstream speed that is exactly three times the correctly computed upstream speed over 5 hours. Only 72 km corresponds to 14.4 km/h sustained for 5 hours.

Common Pitfalls:
Some learners confuse the relation and assume upstream speed is three times downstream speed. Others miscalculate 12 / 2.5 or incorrectly double instead of tripling the upstream speed. It is important to carefully read the phrase "downstream swimming rate is thrice of her upstream swimming rate" and perform precise arithmetic when converting between speed, time, and distance.

Final Answer:
The woman will cover 72 km in 5 hours while swimming downstream.