To determine how long it would take Jaime to finish 21 problems, we can set up a proportion based on the rate at which he completes problems.

First, find Jaime's rate of completing problems:

$\text{Rate} = \frac{15 \text{ problems}}{2.5 \text{ hours}} = \frac{15}{2.5} = 6 \text{ problems per hour}$

Next, use this rate to find the time needed to complete 21 problems:

$\text{Time} = \frac{21 \text{ problems}}{6 \text{ problems per hour}} = \frac{21}{6} = 3.5 \text{ hours}$

So, it would take Jaime 3.5 hours to finish 21 problems.

Would you like more details or have any questions? Here are some related questions:

1. What is the average rate of problem-solving if Jaime took different amounts of time each hour?
2. How long would it take Jaime to solve 30 problems at the same rate?
3. If Jaime improves his speed and solves 21 problems in 3 hours, what is his new rate?
4. How many problems can Jaime solve in 1 hour if he doubles his current rate?
5. How many problems would Jaime solve in 4 hours at his current rate?

Tip: When dealing with proportions, always ensure that the units are consistent across the equation.