Problem 79 - College Algebra and Calculus: An Applied Approach

Question

While traveling on the Pennsylvania Turnpike, you pass milepost 57 near Pittsburgh, then milepost 236 near Gettysburg. How far do you travel during that time period?

Step-by-Step Solution

Answer

The total distance travelled is 179 miles.

Step 1: Identify start and end mileposts

Firstly, identify the starting and ending mileposts. The starting milepost is 57 and the ending milepost is 236.

Step 2: Calculate the distance travelled

In order to find out the distance travelled, subtract the starting milepost from the ending milepost. This would involve performing the arithmetic operation: \(236 - 57\).

Key Concepts

Mileposts

Mileposts, also known as mile markers, are roadside signs that indicate the distance traveled on a particular road or highway. They are fundamental to understanding how far one has traveled. In our exercise, mileposts serve as fixed reference points along the Pennsylvania Turnpike, indicating the mileage from a specific origin point.

For instance, if you are traveling and pass by milepost 57, it means you are 57 miles away from the starting point of this route. Similarly, reaching milepost 236 signifies that you've traveled 236 miles since the beginning of the highway.

Understanding mileposts can help travelers keep track of their journey and estimate distances between different locations.

Arithmetic Operation

Arithmetic operations are basic mathematical processes such as addition, subtraction, multiplication, and division. In the context of our exercise, the arithmetic operation of subtraction is used to calculate the distance traveled between two milepost markers.

The process involves taking the number indicated by the ending milepost and subtracting the number from the starting milepost.

• The ending milepost is 236
• The starting milepost is 57
• Subtraction calculation: \( 236 - 57 = 179 \)

By performing this subtraction, the operation provides you with the total number of miles traveled, which in this case is 179 miles.

Such arithmetic operations are simple yet crucial for solving real-world problems like this one.

Travel Distance

Travel distance is the measure of how far an object, such as a vehicle, has moved along a path. Getting a clear understanding of travel distance is crucial for planning journeys and keeping track of how much distance still needs to be covered.

In the exercise context, travel distance is calculated by finding the difference between consecutive mileposts. The initial milepost provides the starting point, while the final milepost indicates the ending point of the travel.

• The initial distance covered at milepost 57
• The ending distance covered at milepost 236
• Meaning total travel distance is 179 miles

Knowing the distance helps travelers manage their fuel, estimate travel times, and prepare for stops or overnight stays along the way. Understanding travel distance can also aid in budgeting travel expenses more effectively.