Julia can finish a 20-mile bike ride in 1.2 hours. Katie can finish the same bike ride in 1.6 hours. To the nearest tenth of a mile, how much faster does Julia ride than Katie?

A. 4.2 mph
B. 8.0 mph
C. 12.5 mph
D. 15.4 mph



Answer :

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].