Question
Anna drove at a constant rate of 63 miles per hour for 3.2 hours. She determined she drove 201.6 miles. Which best explains the reasonableness of Anna’s answer?
There are three digits to the left of the decimal in the factors and three digits to the left of the decimal in the answer, so Anna’s answer is reasonable.
There is one digit to the right of the decimal in the factors and one digit to the right of the decimal in the answer, so Anna’s answer is reasonable.
Anna’s answer is reasonable because 60 times 3 is 180, and 180 is reasonably close to 201.6.
Anna’s answer is reasonable because 70 times 4 is 280, and 280 is reasonably close to 201.6.
There are three digits to the left of the decimal in the factors and three digits to the left of the decimal in the answer, so Anna’s answer is reasonable.
There is one digit to the right of the decimal in the factors and one digit to the right of the decimal in the answer, so Anna’s answer is reasonable.
Anna’s answer is reasonable because 60 times 3 is 180, and 180 is reasonably close to 201.6.
Anna’s answer is reasonable because 70 times 4 is 280, and 280 is reasonably close to 201.6.
Answers
GPT-4o mini
To assess the reasonableness of Anna's calculated distance of 201.6 miles using the formula \( \text{Distance} = \text{Rate} \times \text{Time} \), we can estimate the computation:
- Anna drove at a constant rate of 63 miles per hour for 3.2 hours.
- If we simplify the calculation, we can round the rate to 60 mph and the time to 3 hours:
\[
\text{Estimated Distance} = 60 \, \text{miles per hour} \times 3 \, \text{hours} = 180 \, \text{miles}
\]
This estimate of 180 miles is reasonably close to 201.6 miles, suggesting that Anna's calculated distance seems reasonable.
Looking at the provided options, the correct rationale to support the reasonableness of Anna’s answer is:
**Anna’s answer is reasonable because 60 times 3 is 180, and 180 is reasonably close to 201.6.**
- Anna drove at a constant rate of 63 miles per hour for 3.2 hours.
- If we simplify the calculation, we can round the rate to 60 mph and the time to 3 hours:
\[
\text{Estimated Distance} = 60 \, \text{miles per hour} \times 3 \, \text{hours} = 180 \, \text{miles}
\]
This estimate of 180 miles is reasonably close to 201.6 miles, suggesting that Anna's calculated distance seems reasonable.
Looking at the provided options, the correct rationale to support the reasonableness of Anna’s answer is:
**Anna’s answer is reasonable because 60 times 3 is 180, and 180 is reasonably close to 201.6.**