Explain why a student who runs 3/4 mile in 6 minutes is faster than a student who runs 1/2 mile in 5 minutes.

Question

5 minutes.
The student who runs 2 mile in 6 minutes will run 1 mile in (?) minutes if the rate is constant

The student who runs 1/2 mile in 5 minutes will run 1 mile in (?) minutes if the rate is constant

Answer 1

To determine who is faster between the two students, we can calculate their speeds in miles per minute.

Student 1: Runs 3/4 mile in 6 minutes

1. Speed Calculation: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3/4 \text{ mile}}{6 \text{ minutes}} = \frac{3}{4} \div 6 = \frac{3}{4} \times \frac{1}{6} = \frac{3}{24} = \frac{1}{8} \text{ miles per minute} \]

2. Time to run 1 mile: \[ \text{Time} = \frac{1 \text{ mile}}{\frac{1}{8} \text{ miles per minute}} = 1 \times 8 = 8 \text{ minutes} \]

Student 2: Runs 1/2 mile in 5 minutes

1. Speed Calculation: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1/2 \text{ mile}}{5 \text{ minutes}} = \frac{1}{2} \div 5 = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \text{ miles per minute} \]

2. Time to run 1 mile: \[ \text{Time} = \frac{1 \text{ mile}}{\frac{1}{10} \text{ miles per minute}} = 1 \times 10 = 10 \text{ minutes} \]

Comparison

• Student 1 can run 1 mile in 8 minutes.
• Student 2 can run 1 mile in 10 minutes.

Thus, Student 1 is faster than Student 2 because they take less time to run a mile.

Answers to Specific Questions

1. The student who runs 3/4 mile in 6 minutes will run 1 mile in 8 minutes.
2. The student who runs 1/2 mile in 5 minutes will run 1 mile in 10 minutes.