To determine how many puzzles Shanee can complete in 15 hours, we start by calculating her rate of completing puzzles.
1. Determine the time taken to complete 3 puzzles:
Shanee takes [tex]\( 4 \frac{1}{2} \)[/tex] hours to complete 3 puzzles. We convert [tex]\( 4 \frac{1}{2} \)[/tex] hours into a decimal:
[tex]\[
4 \frac{1}{2} \text{ hours} = 4.5 \text{ hours}
\][/tex]
2. Calculate the rate of completing puzzles:
Her rate of completing puzzles is found by dividing the number of puzzles by the time taken:
[tex]\[
\text{Rate} = \frac{\text{Number of puzzles}}{\text{Time taken}} = \frac{3 \text{ puzzles}}{4.5 \text{ hours}} = 0.6667 \text{ puzzles per hour}
\][/tex]
3. Calculate the number of puzzles completed in 15 hours:
To find the number of puzzles she can complete in 15 hours, we multiply her rate by 15 hours:
[tex]\[
\text{Number of puzzles in 15 hours} = \text{Rate} \times \text{Total time} = 0.6667 \text{ puzzles per hour} \times 15 \text{ hours} = 10 \text{ puzzles}
\][/tex]
Therefore, working at the same rate, Shanee can complete 10 puzzles in 15 hours. The correct answer is:
a) 10 puzzles
