Understanding the Distance Traveled by Two Cars at Constant Speed

In this article, we delve into the scenario where two cars travel at the same constant speed. By analyzing the given data, you will be able to calculate the distances each car travels and learn how to apply the distance formula using these examples.

Case Study Overview

Let's explore a practical example involving two cars traveling at constant speeds. We will calculate the distance each car travels and understand the relationship between speed, time, and distance.

First Car's Journey

The first car travels for 10 minutes at a constant speed. To calculate the distance traveled, we use the distance formula: [ text{Distance} text{Speed} times text{Time} ]

The speed is given as 63.5293 mph. Rewriting the speed in miles per minute, we get:

[ 63.5293 , text{mph} frac{63.5293}{60} , text{miles per minute} approx 1.05882 , text{miles per minute} ]

Now, calculate the distance for 10 minutes:

[ text{Distance} 1.05882 times 10 approx 10.5882 , text{miles} ]

Thus, the first car travels approximately 10.5882 miles.

Second Car's Journey

The second car travels for 27 minutes at the same constant speed. Using the same formula and the transformed speed:

[ text{Distance} 1.05882 times 27 approx 28.5882 , text{miles} ]

Thus, the second car travels approximately 28.5882 miles.

Comparing the Distances

Interestingly, there is a difference in the distances traveled by the two cars, which is 18 miles. Let's break down this variation:

1. **Time Difference:** The second car travels for an additional 17 minutes (27 minutes - 10 minutes 17 minutes).

2. **Speed Consistency:** Both cars travel at the same speed of 63.5293 mph, or 1.05882 miles per minute.

3. **Distance Calculation:** The extra 17 minutes results in 17 minutes × 1.05882 miles per minute 18.0000 miles, which aligns with the given data.

Verification and Conclusion

To verify the calculations, let's summarize:

First Car's Distance: 10.5882 miles Second Car's Distance: 28.5882 miles Difference: 28.5882 - 10.5882 18 miles

Both the examples provided and the derived outputs align perfectly, confirming the accuracy of the calculations.

Key Takeaways

The distance formula [ text{Distance} text{Speed} times text{Time} ] is a fundamental concept in physics and mathematics. Understanding the relationships between speed, time, and distance is crucial for solving real-world problems. The constant speed scenario presented here helps in grasping the practical application of the distance formula.

Resources for Further Learning

To enhance your understanding of distance, speed, and time calculations, consider exploring the following resources:

Distance Formula - Basic Explanation Constant Speed Problems Real-world Examples of Speed and Distance

By mastering these concepts, you will be better equipped to tackle similar problems and understand the underlying principles.