Question

Sarah jogs 4 12 miles in 34 of an hour. What is her average speed in miles per hour?

Answer 1

To find Sarah's average speed in miles per hour, we need to divide the distance she jogged by the time it took her.

1. **Convert the distance**:
Sarah jogged \( 4 \frac{1}{2} \) miles, which can be converted into an improper fraction:
\[
4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \text{ miles}
\]

2. **Convert the time**:
The time she jogged is \( \frac{3}{4} \) of an hour.

3. **Calculate the average speed**:
The average speed is calculated by dividing the distance by the time:
\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{9}{2} \text{ miles}}{\frac{3}{4} \text{ hours}}
\]
To divide by a fraction, we multiply by the reciprocal:
\[
\text{Average speed} = \frac{9}{2} \times \frac{4}{3}
\]

4. **Perform the multiplication**:
\[
= \frac{9 \times 4}{2 \times 3} = \frac{36}{6} = 6 \text{ miles per hour}
\]

Thus, Sarah's average speed is \( \boxed{6} \) miles per hour.