A runner is training for a half marathon. On Wednesday, she ran 6 miles in 50 minutes. On Thursday, she ran 4 miles in 32 minutes. Assuming she ran at a constant rate each day, on which day did sh run faster? By how much faster did she run?

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To determine on which day the runner was faster and by how much, we'll calculate her average speed for each day.

### 1. Calculate the Average Speed

**Average Speed** is given by the formula:

$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
$$

#### **Wednesday**
- **Distance:** 6 miles
- **Time:** 50 minutes

First, convert the time to hours to calculate speed in miles per hour (mph):

$$
50 \text{ minutes} = \frac{50}{60} \text{ hours} \approx 0.833 \text{ hours}
$$

$$
\text{Speed}_{\text{Wednesday}} = \frac{6 \text{ miles}}{0.833 \text{ hours}} \approx 7.2 \text{ mph}
$$

#### **Thursday**
- **Distance:** 4 miles
- **Time:** 32 minutes

Convert the time to hours:

$$
32 \text{ minutes} = \frac{32}{60} \text{ hours} \approx 0.533 \text{ hours}
$$

$$
\text{Speed}_{\text{Thursday}} = \frac{4 \text{ miles}}{0.533 \text{ hours}} \approx 7.5 \text{ mph}
$$

### 2. Compare the Speeds

- **Wednesday:** ~7.2 mph
- **Thursday:** ~7.5 mph

**Thursday's speed (7.5 mph) is higher than Wednesday's speed (7.2 mph).**

### 3. Calculate the Difference in Speed

$$
\text{Difference} = 7.5 \text{ mph} - 7.2 \text{ mph} = 0.3 \text{ mph}
$$

### **Conclusion**

- **Day Faster:** **Thursday**
- **By How Much:** **0.3 mph faster**
On Thursday, the runner was faster by 0.3 mph.

A runner is training for a half marathon. On Wednesday, she ran 6 miles in 50 minutes. On Thursday, she ran 4 miles in 32 minutes. Assuming she ran at a constant rate each day, on which day did sh run faster? By how much faster did she run?

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