Calculating the Mean Speed for a Mileage Journey: A Comprehensive Guide

Calculating the mean speed for a journey is a common task for both travelers and transportation professionals. In this article, we explain the method using a specific scenario: a car that travels 20 miles at 30 mph, then 10 miles at 60 mph. We will walk through the steps to find the mean speed for the entire journey.

Understanding Mean Speed

The mean speed, or average speed, is calculated using the formula:

( text{Mean Speed} frac{text{Total Distance}}{text{Total Time}} )

Step-by-Step Calculation

Let's break down the journey step-by-step to find the mean speed.

Step 1: Calculate the Total Distance

The total distance of the journey is the sum of the individual segments:

(20 , text{miles} 10 , text{miles} 30 , text{miles} )

Step 2: Calculate the Time Taken for Each Segment

To find the time taken for each segment, we use the formula:

( text{Time} frac{text{Distance}}{text{Speed}} )

For the first segment: 20 miles at 30 mph ( text{Time}_{1} frac{20 , text{miles}}{30 , text{mph}} frac{2}{3} , text{hours} approx 0.67 , text{hours} ) For the second segment: 10 miles at 60 mph ( text{Time}_{2} frac{10 , text{miles}}{60 , text{mph}} frac{1}{6} , text{hours} approx 0.17 , text{hours} )

Step 3: Calculate the Total Time

The total time is the sum of the times for each segment:

( text{Total Time} frac{2}{3} , text{hours} - frac{1}{6} , text{hours} )

To add these fractions, find a common denominator, which is 6:

( frac{2}{3} frac{4}{6} )

Now, add the fractions:

( text{Total Time} frac{4}{6} frac{1}{6} frac{5}{6} , text{hours} )

Step 4: Calculate the Mean Speed

Now, use the mean speed formula:

( text{Mean Speed} frac{30 , text{miles}}{frac{5}{6} , text{hours}} 30 , text{miles} times frac{6}{5} 36 , text{mph} )

Therefore, the mean speed for the entire journey is 36 mph.

Understanding Common Sense in Speed Calculation

When calculating mean speed, it’s essential to consider the nature of the journey. For instance, traveling 30 miles per hour means you’re covering a half-mile every minute. For 20 miles, that would take 40 minutes. Traveling 60 miles per hour means you’re covering a mile every minute, so for 10 miles, it would take 10 minutes.

By combining these times (40 10 50 minutes), we get the total duration. To find the average speed, we divide the total distance (30 miles) by the total time (50 minutes or 0.833 hours).

( text{Average Speed} frac{30 , text{miles}}{frac{50}{60} , text{hours}} frac{30 , text{miles}}{frac{5}{6} , text{hours}} 36 , text{mph} )

This method provides a practical approach to understanding and calculating average speeds.

Conclusion

Understanding how to calculate mean speed is crucial for both personal and professional applications, from planning road trips to optimizing transportation schedules. By following the steps outlined in this article, you can easily calculate the mean speed for any given journey.

Related Keywords

mean speed, travel time, average speed