Comparing Average Speeds of Cyclists: A Real-World Application

In many real-world scenarios, understanding the average speed of individuals is crucial. This problem involves two cyclists, Amy and Bill, traveling from their neighborhood to their school, which is 14.4 kilometers away. We will calculate the average speeds of both cyclists and determine how much faster Amy's average speed is compared to Bill's.

Introduction to Cyclists' Trip

Bill and Amy are planning to bike from their neighborhood to school, a distance of 14.4 kilometers. Amy arrives at school in 30 minutes, while Bill arrives 15 minutes after Amy.

Calculating Amy's Average Speed

Let's first calculate Amy's average speed. The distance to school is 14.4 kilometers, and the time taken by Amy is 30 minutes, which is equivalent to 0.5 hours (since 30 minutes 0.5 hours).

The formula for calculating average speed is:

Average Speed Distance / Time

Plugging the values for Amy:

Amy's speed 14.4 km / 0.5 hr 28.8 km/hr

Calculating Bill's Average Speed

Bill arrives 15 minutes after Amy. Therefore, the total time taken by Bill is 30 minutes 15 minutes 45 minutes, which is equivalent to 0.75 hours (since 45 minutes 0.75 hours).

Using the same formula for Bill's average speed:

Bills speed 14.4 km / 0.75 hr 19.2 km/hr

Determining the Speed Difference

To find out how much faster Amy's average speed is compared to Bill's, we subtract Bill's speed from Amy's speed:

Difference in speed Amy's speed - Bill's speed

Difference in speed 28.8 km/hr - 19.2 km/hr 9.6 km/hr

Therefore, Amy's average speed is 9.6 km/hr faster than Bill's.

Conclusion

The problem of comparing Amy and Bill's average speeds highlights the importance of understanding and applying basic speed calculations in real-world scenarios. By using the formula for average speed, we can easily determine the difference in their speeds, which can be crucial in various applications, such as planning routes, estimating travel times, and understanding the efficiency of cyclists.

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This article draws inspiration from the given problem and solution, emphasizing real-world applications of speed calculations.