To determine whose grading shows a proportional relationship between the number of tests graded and the time spent grading, we need to calculate the rate at which each person grades science and math tests.
Mr. Coelho:
-
Science Tests:
- 25 tests in 50 minutes.
- Rate = \( \frac{25 \text{ tests}}{50 \text{ minutes}} = \frac{1 \text{ test}}{2 \text{ minutes}} \) or 0.5 tests per minute.
-
Math Tests:
- 30 tests in 40 minutes.
- Rate = \( \frac{30 \text{ tests}}{40 \text{ minutes}} = \frac{3 \text{ tests}}{4 \text{ minutes}} = 0.75 \text{ tests per minute} \).
Mr. Coelho's grading rates are not consistent (0.5 tests/min for science and 0.75 tests/min for math), indicating a non-proportional relationship.
Ms. Steiner:
-
Science Tests:
- 20 tests in 50 minutes.
- Rate = \( \frac{20 \text{ tests}}{50 \text{ minutes}} = \frac{2 \text{ tests}}{5 \text{ minutes}} = 0.4 \text{ tests per minute} \).
-
Math Tests:
- 12 tests in 30 minutes.
- Rate = \( \frac{12 \text{ tests}}{30 \text{ minutes}} = \frac{2 \text{ tests}}{5 \text{ minutes}} = 0.4 \text{ tests per minute} \).
Ms. Steiner's grading rates are consistent across both subjects, showing a proportional relationship (both are 0.4 tests/min).
Conclusion:
Based on this analysis, the answer is:
B. only Ms. Steiner's grading