Let's solve each part of the problem step by step.

Part a: How many math problems can Jaime finish in 8 hours?

First, find the rate at which Jaime finishes math problems.

• Rate of completing problems: $\text{Rate} = \frac{15 \text{ problems}}{2.5 \text{ hours}} = \frac{15}{2.5} = 6 \text{ problems per hour}$

Now, use this rate to determine how many problems he can finish in 8 hours:

• Problems in 8 hours: $6 \text{ problems/hour} \times 8 \text{ hours} = 48 \text{ problems}$

Part b: How long would it take him to finish 21 problems?

Use the rate found earlier to determine the time needed to finish 21 problems:

• Time required: $\text{Time} = \frac{21 \text{ problems}}{6 \text{ problems/hour}} = 3.5 \text{ hours}$

Summary:

• Part a: Jaime can finish 48 problems in 8 hours.
• Part b: It would take Jaime 3.5 hours to finish 21 problems.

Would you like more details or have any questions?

Here are 5 related questions:

1. How many problems can Jaime finish in 5 hours at the same rate?
2. If Jaime worked for 3 hours and finished 20 problems, what would his new rate be?
3. How many problems would Jaime finish in 12 hours if he increased his speed by 20%?
4. How long would it take Jaime to finish 100 problems at the current rate?
5. What would the time be to finish 50 problems if Jaime worked 25% faster?

Tip: When solving rate problems, always check the units (e.g., problems per hour) to ensure your calculations are consistent.