Question
Nate’s work to solve a math problem is shown below.
Problem: Leona traveled 25 miles in Two-thirds of an hour. What was her average speed in miles per hour?
Step 1:
25 divided by two-thirds = r
Step 2:
StartFraction 1 Over 25 EndFraction times two-thirds = r
Answer:
StartFraction 2 Over 75 EndFraction = r
What was Nate’s first error?
Problem: Leona traveled 25 miles in Two-thirds of an hour. What was her average speed in miles per hour?
Step 1:
25 divided by two-thirds = r
Step 2:
StartFraction 1 Over 25 EndFraction times two-thirds = r
Answer:
StartFraction 2 Over 75 EndFraction = r
What was Nate’s first error?
Answers
GPT-4o mini
Nate's first error occurs in Step 1 when he attempts to divide 25 by two-thirds. The correct operation to find average speed is to divide the total distance traveled (25 miles) by the total time taken (two-thirds of an hour).
The correct calculation for average speed (r) should be:
\[
r = \frac{25 \text{ miles}}{\frac{2}{3} \text{ hour}}
\]
To divide by a fraction, you multiply by its reciprocal:
\[
r = 25 \times \frac{3}{2}
\]
This means Nate's initial setup of dividing 25 by two-thirds was incorrect in the context of finding average speed. Correctly applying the division by a fraction (which results in multiplication by the reciprocal) would have led him to the correct formula for calculating average speed.
The correct calculation for average speed (r) should be:
\[
r = \frac{25 \text{ miles}}{\frac{2}{3} \text{ hour}}
\]
To divide by a fraction, you multiply by its reciprocal:
\[
r = 25 \times \frac{3}{2}
\]
This means Nate's initial setup of dividing 25 by two-thirds was incorrect in the context of finding average speed. Correctly applying the division by a fraction (which results in multiplication by the reciprocal) would have led him to the correct formula for calculating average speed.