To determine how long it would take Jaime to finish 21 math problems, we can use the concept of unit rate (problems per hour) and then scale it up to 21 problems.

Step 1: Calculate the rate of problems per hour

Jaime finishes 15 problems in 2.5 hours. The rate at which he completes the problems is:

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

Step 2: Determine the time to finish 21 problems

Now that we know he completes 6 problems per hour, we can find out how long it would take him to finish 21 problems by dividing the number of problems by his rate:

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

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

Would you like more details on this problem or have any other questions?

Here are 5 related questions to consider:

1. How long would it take Jaime to finish 30 problems at the same rate?
2. If Jaime increases his speed and finishes 15 problems in 2 hours, how long would it take him to finish 21 problems?
3. How many problems can Jaime finish in 5 hours at his original rate?
4. If Jaime takes a 10-minute break for every hour he works, how much total time will he spend to finish 21 problems, including breaks?
5. How would the time change if Jaime started solving problems 20% faster?

Tip: Understanding unit rates (like problems per hour) can simplify solving many proportional reasoning problems in math.