Question
Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.
Answers
GPT-4o mini
The best explanation for Sebastian's actual solution is:
**The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.**
This explanation is valid because he rounded the average rate (43.5 mph) down to 40 mph and the time (2.2 hours) down to 2 hours for estimating. The estimate of 80 miles (40 mph x 2 hours) is less than the actual product, which is calculated from the exact values, leading to 95.7 miles. The actual distance indeed falls close to the estimate but is higher due to the rounding down of both factors.
**The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.**
This explanation is valid because he rounded the average rate (43.5 mph) down to 40 mph and the time (2.2 hours) down to 2 hours for estimating. The estimate of 80 miles (40 mph x 2 hours) is less than the actual product, which is calculated from the exact values, leading to 95.7 miles. The actual distance indeed falls close to the estimate but is higher due to the rounding down of both factors.