How Long Does It Take to Cover 100 Miles at 80 mph and 75 mph?

When you want to calculate the time it takes to travel a certain distance at a specific speed, you can follow a simple formula: time distance ÷ speed. This formula is both fundamental and practical, making it a cornerstone of basic physics and mathematics. In this article, we explore the calculations for two different scenarios: traveling 100 miles at 80 mph and 75 mph. Let's break down the process step-by-step to ensure clarity and accuracy.

100 Miles at 80 mph

First, let's consider the scenario where we are traveling 100 miles at a speed of 80 mph. Using the formula time distance ÷ speed, we can perform the calculation as follows:

Substitute the values into the formula: time 100 miles ÷ 80 mph Perform the division: 100 ÷ 80 1.25 hours Convert the decimal to hours and minutes: 1.25 hours 1 hour and 15 minutes

Therefore, it will take 1 hour and 15 minutes to cover 100 miles at a speed of 80 mph. This method of conversion is straightforward and ensures that you have a clear understanding of the time required for the journey.

100 Miles at 75 mph

Let's now turn to the second scenario, where the distance is the same (100 miles), but the speed is different (75 mph). Again, we will use the formula time distance ÷ speed to determine the time taken:

Substitute the values into the formula: time 100 miles ÷ 75 mph Perform the division: 100 ÷ 75 1.3333... hours (repeating) Convert the decimal to hours and minutes: 1.3333 hours 1 hour and 20 minutes

Hence, traveling 100 miles at 75 mph will take approximately 1 hour and 20 minutes. This calculation can also be broken down using algebraic methods:

Distance formula: distance speed x time Substitute the known values: 100 75 x time Solve for time: time 100 ÷ 75 1.3333... hours 1 hour and 20 minutes

As an alternative, you can use the arithmetic method to find the remaining distance after the first hour and convert the remaining fraction of an hour into minutes:

Calculate the distance covered in the first hour: 75 miles Find the remaining distance: 100 - 75 25 miles Convert the remaining distance to a fraction of the speed: 25 miles ÷ 75 mph 1/3 hour Convert 1/3 hour to minutes: 1/3 hour × 60 minutes/hour 20 minutes Therefore, the total time is 1 hour 20 minutes 1 hour and 20 minutes

Both methods lead to the same result, which confirms the accuracy of our calculations. Whether you prefer to use the formula or break it down into smaller steps, the key is to ensure that your arithmetic is correct and your units are consistent.

Conclusion

Understanding and applying the speed, distance, and time formula is crucial for various real-world applications, from travel planning to scientific calculations. By utilizing this formula, you can accurately determine the time required for a journey, regardless of the distance and speed involved.

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Additional Resources

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