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?
Distance (mi) Rate (mph) Time (hr)
Julia 20 1.2
Katie 20 1.6
A. 4.2 mph
B. 8.0 mph
C. 12.5 mph
D. 15.4 mph
Answer (1)
Calculate Julia's speed: 1.2 20 = 16.666... mph.
Calculate Katie's speed: 1.6 20 = 12.5 mph.
Find the difference in their speeds: 16.666... − 12.5 = 4.1666... mph.
Round the difference to the nearest tenth: 4.2 mph.
Explanation
Calculate Julia's Speed First, we need to calculate Julia's speed. We know she travels 20 miles in 1.2 hours. To find her speed, we use the formula: s p ee d = t im e d i s t an ce So, Julia's speed is: s p ee d J u l ia = 1.2 20
Calculate Katie's Speed Next, we calculate Katie's speed. She travels 20 miles in 1.6 hours. Using the same formula: s p ee d = t im e d i s t an ce Katie's speed is: s p ee d K a t i e = 1.6 20
Find the Difference in Speeds Now, we find the difference in their speeds by subtracting Katie's speed from Julia's speed: d i ff ere n ce = s p ee d J u l ia − s p ee d K a t i e = 1.2 20 − 1.6 20 We can calculate this difference: d i ff ere n ce = 1.2 20 − 1.6 20 = 16.666... − 12.5 = 4.1666...
Round to the Nearest Tenth Finally, we round the difference to the nearest tenth of a mile per hour: 4.1666... ≈ 4.2 So, Julia rides approximately 4.2 mph faster than Katie.
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 plan stops accordingly. Similarly, in sports, comparing the speeds of athletes can provide insights into their performance and help coaches develop effective strategies. This problem demonstrates a simple application of calculating and comparing speeds, which is a fundamental concept in physics and everyday life.
