A boat travels 12 km in 1 hour in still water (so v = 12 km/h). It takes three times as long to cover the same 12 km against the current. What is the speed of the current (in km/h)?

Introduction / Context:
This is a direct application of upstream speed determination from a given time factor relative to still water performance. When the upstream time is some multiple of the still-water time for the same distance, we can infer the upstream speed and then the current.

Given Data / Assumptions:

• Still water speed v = 12 km/h.
• Distance D = 12 km.
• Upstream time is three times the still-water time for D (which is 1 hour in still water).

Concept / Approach:
Still-water time for 12 km is 1 h, so the upstream time is 3 h. Therefore, upstream speed = distance / time = 12/3 = 4 km/h. Since upstream speed equals v − c, solve c = v − 4.

Step-by-Step Solution:

Verification / Alternative check:
With c = 8, downstream speed is 20 km/h and upstream is 4 km/h. To cover 12 km upstream at 4 km/h takes 3 h, which is three times the still-water time of 1 h.

Why Other Options Are Wrong:
12 km/h would imply zero or negative upstream capability; 6 or 7 km/h do not yield an upstream time exactly three times the still-water time.

Common Pitfalls:
Mistaking the relation between time and speed; the triple time factor applies to time, not speed, and thus speed is one-third in that leg.

Final Answer:
8 km/h