To find out how much faster Julia rides than Katie, we need to calculate the speeds of both Julia and Katie first, and then find the difference between these speeds. We are given the distance and the times they take to cover that distance.
1. Distance for both: [tex]\( 20 \)[/tex] miles
2. Time for Julia: [tex]\( 1.2 \)[/tex] hours
3. Time for Katie: [tex]\( 1.6 \)[/tex] hours
We use the formula for speed, which is [tex]\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)[/tex].
### Step-by-Step Calculation:
1. Speed of Julia:
[tex]\[
\text{Speed}_\text{Julia} = \frac{20 \text{ miles}}{1.2 \text{ hours}} = 16.67 \text{ mph} \, (\text{rounded to two decimal places})
\][/tex]
2. Speed of Katie:
[tex]\[
\text{Speed}_\text{Katie} = \frac{20 \text{ miles}}{1.6 \text{ hours}} = 12.5 \text{ mph}
\][/tex]
3. Difference in their speeds:
[tex]\[
\text{Speed Difference} = \text{Speed}_\text{Julia} - \text{Speed}_\text{Katie}
\][/tex]
[tex]\[
\text{Speed Difference} = 16.67 \text{ mph} - 12.5 \text{ mph} = 4.2 \text{ mph}
\][/tex]
### Conclusion:
Julia rides [tex]\( 4.2 \)[/tex] miles per hour faster than Katie. This is rounded to the nearest tenth, hence the answer is [tex]\( 4.2 \text{ mph} \)[/tex].
Thus, to answer the question: Julia rides [tex]\( 4.2 \)[/tex] miles per hour faster than Katie.
