Julia can finish a 20-mile bike ride in 1.2 hours. Katie can finish the same bike ride in 1.0 hours. How much faster does Katie ride than Julia?
| | Distance (mi) | Rate (mph) | Time (hr) |
| :---- | :------------ | :--------- | :-------- |
| Julia | 20 | | 1.2 |
| Katie | 20 | | 1.0 |
A. 4.2 mph
B. 8.0 mph
C. 12.5 mph
D. 15.4 mph
Answer (2)
Katie rides 3.33 mph faster than Julia, with Julia's speed being 16.67 mph and Katie's speed being 20 mph. This difference is calculated by subtracting Julia's speed from Katie's speed. The correct answer is not in the multiple choice options provided, so it can be reported as 3.33 mph.
;
Calculate Julia's speed: s p ee d J u l ia = 1.2 20 = 16.67 mph .
Calculate Katie's speed: s p ee d K a t i e = 1.0 20 = 20 mph .
Find the difference in speeds: s p ee d d i ff ere n ce = 20 − 16.67 = 3.33 mph .
Katie rides faster than Julia by 3.33 mph .
Explanation
Understanding the Problem We are given that Julia can finish a 20-mile bike ride in 1.2 hours, and Katie can finish the same ride in 1.0 hours. We want to find out how much faster Katie rides than Julia.
Calculating Julia's Speed First, we need to calculate Julia's speed. Speed is calculated by dividing the distance by the time. So, Julia's speed is:
Julia's Speed s p ee d J u l ia = t im e d i s t an ce = 1.2 hours 20 miles s p ee d J u l ia = 16.67 mph
Calculating Katie's Speed Next, we calculate Katie's speed using the same formula:
Katie's Speed s p ee d K a t i e = t im e d i s t an ce = 1.0 hours 20 miles s p ee d K a t i e = 20 mph
Finding the Speed Difference Now, we find the difference between Katie's speed and Julia's speed to determine how much faster Katie rides:
Speed Difference s p ee d d i ff ere n ce = s p ee d K a t i e − s p ee d J u l ia = 20 mph − 16.67 mph s p ee d d i ff ere n ce = 3.33 mph
Conclusion Therefore, Katie rides approximately 3.33 mph faster than Julia.
Examples
Understanding relative speeds is useful in many real-world scenarios. For example, if you're planning a road trip with friends, knowing the different driving speeds can help you estimate arrival times and coordinate stops. Similarly, in sports, comparing the speeds of athletes can inform training strategies and predict performance outcomes. This problem demonstrates a basic application of speed calculations, which is a fundamental concept in physics and everyday life.
