Question

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.

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**.