7.2. The road from point A to point B first goes uphill and then downhill. A cat takes 2 hours and 12 minutes to travel from A to B, and the return trip takes 6 minutes longer. The cat's speed going uphill is 4 km/h, and downhill is 5 km/h. How many kilometers is the distance from A to B? (Provide a complete solution, not just the answer.)
Solution: When a cat goes uphill, it takes 15 minutes for 1 km, and when it goes downhill, it takes 12 minutes. That is, when the direction changes, the time spent on 1 km changes by 3 minutes. Since the cat spent 6 minutes more on the return trip, the uphill section on the return trip is 2 km longer.

Let the length of the uphill section on the way from A to B be $x$. Then we can set up the equation $15 x + 12(x + 2) = 132$, from which $x = 4$. Therefore, the total distance is $x + (x + 2) = 4 + 6 = 10$ km.

Comment: Other solutions are possible. For example, a system of equations could have been set up and solved immediately. Or it could have been proven that the difference between the two sections of the path is 2 km, then the answer could be guessed, and then its uniqueness could be proven.

Criteria: Only the answer - 0 points.

Answer with verification - 1 point.

Correct system of equations - 2 points.

Proven that the difference between the two sections of the path is 2 km - 1 point.