Sure, let's explore the problem step-by-step to find out the rates at which Maya and Amy solve puzzles and determine who would finish first if they had to solve the same number of puzzles.
### Step 1: Calculate the Rate at Which Each Student Solves Puzzles
Maya's Rate:
- Maya takes 30 minutes to solve 5 puzzles.
- To find the time it takes for Maya to solve one puzzle, we divide the total time by the number of puzzles:
[tex]\[
\text{Maya's rate} = \frac{\text{Total time}}{\text{Number of puzzles}} = \frac{30 \text{ minutes}}{5 \text{ puzzles}} = 6 \text{ minutes per puzzle}
\][/tex]
Amy's Rate:
- Amy takes 28 minutes to solve 4 puzzles.
- To find the time it takes for Amy to solve one puzzle, we use the same method:
[tex]\[
\text{Amy's rate} = \frac{\text{Total time}}{\text{Number of puzzles}} = \frac{28 \text{ minutes}}{4 \text{ puzzles}} = 7 \text{ minutes per puzzle}
\][/tex]
### Step 2: Compare the Rates
From the calculations above, we found:
- Maya's rate is 6 minutes per puzzle.
- Amy's rate is 7 minutes per puzzle.
### Step 3: Determine Who Finishes First If They Have the Same Number of Puzzles
If Maya and Amy had the same number of puzzles to solve, we can compare how long it would take each of them to finish one puzzle:
- Since Maya takes 6 minutes per puzzle and Amy takes 7 minutes per puzzle, Maya is faster per puzzle.
For example:
- If both Maya and Amy were to solve one puzzle:
- Maya would take [tex]\(6\)[/tex] minutes.
- Amy would take [tex]\(7\)[/tex] minutes.
So, Maya would finish solving the puzzle first.
### Conclusion
If Maya and Amy had the same number of puzzles to solve, Maya would finish first because she solves each puzzle in 6 minutes, while Amy takes 7 minutes per puzzle. Therefore, Maya is quicker in solving the puzzles.
