Sure, let's tackle this step by step:
1. Find Julia's Speed:
- We know Julia finishes the 20-mile bike ride in 1.2 hours.
- To find her speed in miles per hour (mph), we use the formula:
[tex]\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
- Plugging in Julia's distance and time:
[tex]\[
\text{Julia's speed} = \frac{20 \text{ miles}}{1.2 \text{ hours}} = 16.7 \text{ mph}
\][/tex]
2. Find Katie's Speed:
- Katie finishes the same 20-mile bike ride in 1.6 hours.
- Using the same speed formula:
[tex]\[
\text{Katie's speed} = \frac{20 \text{ miles}}{1.6 \text{ hours}} = 12.5 \text{ mph}
\][/tex]
3. Determine How Much Faster Julia Rides:
- To find out how much faster Julia rides compared to Katie, we subtract Katie's speed from Julia's speed:
[tex]\[
\text{Difference} = \text{Julia's speed} - \text{Katie's speed}
\][/tex]
- Plugging in their speeds:
[tex]\[
\text{Difference} = 16.7 \text{ mph} - 12.5 \text{ mph} = 4.2 \text{ mph}
\][/tex]
Thus, Julia rides 4.2 miles per hour faster than Katie. The correct answer is [tex]\( 4.2 \text{ mph} \)[/tex].
