Calculating Elaine’s Average Speed: A Simple and In-Depth Guide

Introduction

In this article, we will solve a common travel problem involving two individuals, Jack and Elaine, and explore the concept of average speed. We will break down the problem step-by-step to find Elaine's average speed for the journey after understanding Jack's travel details. This guide is particularly helpful for those studying math or preparing for exams, as it simplifies complex concepts into manageable parts.

Understanding the Problem

Let's consider the following scenario: Jack travels a distance of 360 km at an average speed of 80 km/h, while Elaine takes 1.5 hours more to complete the same distance.

Step 1: Calculate Jack’s Travel Time

To find Jack's travel time, we use the fundamental formula for time, which is derived from the distance and speed relationship:

Time Distance / Speed

Given the distance (d) is 360 km and the speed (v) is 80 km/h, we calculate:

Time_Jack  360 km / 80 km/h  4.5 hours

Step 2: Determine Elaine’s Travel Time

According to the problem, Elaine takes 1.5 hours more than Jack. Therefore, we add this extra time to Jack's travel time:

Time_Elaine Time_Jack 1.5 hours

Substituting the values, we get:

Time_Elaine  4.5 hours   1.5 hours  6 hours

Step 3: Calculate Elaine’s Average Speed

Now that we have the total travel time for Elaine, we can find her average speed using the distance and time relationship, where speed is the distance divided by the time:

Speed Distance / Time

Given the distance is 360 km and the time is 6 hours, we calculate:

Speed_Elaine  360 km / 6 hours  60 km/h

Conclusion

Therefore, Elaine’s average speed for the whole journey is 60 km/h. This step-by-step approach helps to break down complex problems into simpler components, making it easier to understand and solve similar problems in the future.

Additional Notes and Tips

Note: It's always beneficial to use the appropriate units and carefully check the calculations to ensure accuracy. Understanding the basic principles of distance, time, and speed is crucial for tackling more advanced problems in physics and related fields.