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Chapter 5: Problem 14

Bill left Burlington, Vermont, and traveled to Ottawa, Ontario, the capital of Canada. The distance from Burlington to the Canadian border is approximately 42 miles. The distance from the Canadian border to Ottawa is approximately 280 kilometers. If it took him 4.3 hours to complete the trip, what was his average speed in miles per hour?

Short Answer

Expert verified
The average speed of Bill's journey is approximately \(71.21\) miles per hour.

Step by step solution

01

Convert Kilometers to Miles

The second part of the trip from the Canadian border to Ottawa is given in kilometers. To get the total distance in miles (as the speed must be calculated in miles per hour), this distance needs to be converted into miles. 1 kilometer is approximately 0.621371 miles. Therefore the conversion is done by multiplying \(280\) kilometers by \(0.621371\).
02

Calculate Total Distance

Now, to get the total distance of the trip, add the distance from Burlington to the Canadian border, which is \(42\) miles, to the converted distance from the Canadian border to Ottawa.
03

Calculate Average Speed

The average speed can be calculated by dividing the total distance travelled by the total time taken. In this problem, the total travelling time is \(4.3\) hours. So, the final step is to divide the total distance obtained in step 2 by \(4.3\) to get the average speed in miles per hour.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
In many travel and speed-related problems, converting between units becomes crucial. This ensures consistency across calculations. In the exercise, we convert kilometers into miles because we are calculating speed in miles per hour (mph). The conversion factor between kilometers and miles is approximately 1 kilometer = 0.621371 miles. This means to convert kilometers into miles, you multiply the number of kilometers by 0.621371.

For example, to convert 280 kilometers to miles:
  • Multiply 280 km by 0.621371.
  • This equals approximately 173.984 miles.
Remember, keeping units consistent in a problem is key to avoiding errors in your calculations, especially when calculating distances and speeds.
Distance Calculation
Calculating the total distance in a trip requires you to add up all the parts of the journey. In this task, we have two segments to consider:
  • The distance from Burlington to the Canadian border, which is given in miles.
  • The distance from the border to Ottawa, which is converted from kilometers to miles.
First, recall from the unit conversion section that the 280 kilometers from the Canadian border to Ottawa is equal to 173.984 miles.

To find the total distance:
  • Add the distance from Burlington to the border: 42 miles.
  • Add the converted miles (173.984 miles) to get a total of approximately 215.984 miles.
Now you have the complete distance of the trip, ready for further calculations.
Miles per Hour
When calculating speed, especially when expressed as miles per hour (mph), it is important to understand this represents how many miles are traveled in one hour. Calculating speed requires you to know both the total distance and the total time taken for the journey.

The formula to calculate average speed in miles per hour is:
  • Average speed (mph) = Total distance (miles) 梅 Total time (hours).
This formula will provide you with an understanding of the vehicle's performance over the journey.
Problem-Solving Steps
Solving problems involving average speed can be simplified by following a structured approach. Let's break it down:
  • **Step 1:** Convert any needed measurements into consistent units (e.g., kilometers to miles).
  • **Step 2:** Calculate the total distance, summing up all parts of the journey converted into the same unit.
  • **Step 3:** Use the average speed formula by dividing the total distance by the total time taken.
In our initial example, we performed a conversion, calculated a total distance of 215.984 miles, and used the time of 4.3 hours. By dividing these, we find the average speed in mph. Following careful, orderly steps makes solving these types of problems much easier.

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Most popular questions from this chapter

Lenny's car gets approximately 20 miles per gallon. He is planning a 750 -mile trip. a. About how many gallons of gas should Lenny plan to buy? b. At an average price of \(\$ 4.10\) per gallon, how much should Lenny expect to spend for gas?

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