To find the unit rates for Sam's performance, we need to calculate:
- The number of math questions completed per minute.
- The time taken per math question.
Step 1: Calculate math questions per minute
Sam completed 12 math questions in 24 minutes. To find the unit rate in math questions per minute, we divide the number of questions by the number of minutes:
\[ \text{Questions per minute} = \frac{12 \text{ questions}}{24 \text{ minutes}} = \frac{1}{2} \text{ questions per minute} \]
Step 2: Calculate minutes per math question
To find out how many minutes it took Sam to complete each math question, we divide the total time by the number of questions:
\[ \text{Minutes per question} = \frac{24 \text{ minutes}}{12 \text{ questions}} = 2 \text{ minutes per question} \]
Now we have the rates:
- Sam completes \( \frac{1}{2} \) math questions per minute.
- Sam takes 2 minutes per math question.
Looking at the options provided:
A. \( \frac{1}{2} \) math questions per minute and 2 minutes per math question
B. 2 math questions per minute and 2 minutes per math question
C. \( \frac{1}{2} \) math questions per minute and \( \frac{1}{2} \) minute per math question
D. 2 math questions per minute and \( \frac{1}{2} \) minute per math question
The correct answer is A: \( \frac{1}{2} \) math questions per minute and 2 minutes per math question.