To solve the problem, we need to find out how many math problems Jaime can finish in 8 hours if he finishes 15 math problems in 2.5 hours. This can be done using the concept of ratios.

Step 1: Determine the rate of problems per hour

First, calculate how many math problems Jaime can complete per hour.

$\text{Rate} = \frac{\text{Number of Problems}}{\text{Time in Hours}} = \frac{15 \text{ problems}}{2.5 \text{ hours}} = \frac{15}{2.5} = 6 \text{ problems per hour}$

Step 2: Calculate the total number of problems in 8 hours

Now, use the rate to find out how many problems he can finish in 8 hours.

$\text{Total Problems} = \text{Rate} \times \text{Time} = 6 \text{ problems per hour} \times 8 \text{ hours} = 48 \text{ problems}$

So, Jaime can finish 48 math problems in 8 hours.

Reflection: Using the Other Variable

If you were to scale the other variable, such as changing the number of problems and then finding the corresponding time, your method would involve solving for time given the number of problems. You would still apply the same concept of using the rate, but in reverse.

Would you like further details on this, or do you have any questions?

Here are 5 related questions to consider:

1. How many problems can Jaime complete in 5 hours at the same rate?
2. If Jaime worked for 10 hours, how many problems could he complete?
3. How long would it take Jaime to finish 30 problems?
4. What would be the effect of doubling the time on the number of problems completed?
5. How would the rate change if Jaime completed 30 problems in 5 hours?

Tip: Always determine the rate first when working with problems involving ratios and scaling. It simplifies the process of finding unknown quantities.