Question

Ken Johnson's place is located 17.35 kilometers due west of the center of town on Route 17. Willy Hester's place is located 11.23 kilometers due west of the center of town, also on Route 17. How far from each other do the two neighbors live? A. 6.12 kilometers B. 14.28 kilometers C. 28.58 kilometers D. 45.58 kilometers

Short answer

6.12 kilometers. The correct answer is A.

Step-by-step solution

Understand the Problem

We are given two locations relative to the center of town along Route 17, both in the same direction (due west). We need to find the distance between these two points.

Identify the Known Distances

Ken Johnson's place is 17.35 kilometers west of the center of town. Willy Hester's place is 11.23 kilometers west of the center of town.

Subtract the Shorter Distance from the Longer Distance

To find the distance between the two places, subtract Willy Hester's distance from the center of town from Ken Johnson's distance from the center of town: \(17.35 - 11.23 = 6.12 \text{ kilometers}\)

Choose the Correct Answer

Based on the calculation, the distance between the two places is 6.12 kilometers. Therefore, the correct answer is A.

Key concepts

distance calculation

Distance calculation is an essential concept in math and everyday life. We often need to find out how far one place is from another, just like Ken and Willy's houses.
In our exercise, Ken's house and Willy's house are both located to the west of the center of town, but not at the same distance.
To calculate how far they are from each other, we need to use subtraction. By knowing both distances from a common point (the center of town), we can find the distance between them.

Generally, when two points are located along the same line and share the same direction (both west, north, etc.), the distance between them is found by subtracting the shorter distance from the longer one. This gives us the direct line distance separating the two points.
Using this approach ensures we get the correct and precise calculation, just as seen in Ken and Willy's example.

subtraction

Subtraction is one of the fundamental operations in basic arithmetic. It involves taking one number away from another.
In the given problem, to find the distance between Ken and Willy's houses, we need to subtract Willy's distance from Ken's distance:

This operation can be represented as:
\( 17.35 - 11.23 \)where 17.35 is the distance to Ken's house and 11.23 is the distance to Willy's house.

When we perform the subtraction, we get:
\(17.35 - 11.23 = 6.12\)This result tells us that Ken and Willy's houses are 6.12 kilometers apart.
Remember, the order in which we subtract is crucial. Here, we subtract a smaller number (Willy's distance) from a larger number (Ken's distance) to get a positive distance value.

basic arithmetic

Basic arithmetic forms the foundation of more complex math. It includes addition, subtraction, multiplication, and division.
In our exercise, we mainly used subtraction to find the distance between Ken and Willy's homes.

However, a solid understanding of all basic arithmetic operations is important.
These are some principles of basic arithmetic used in the problem:

• Addition: Combining two or more numbers to find the total.
• Subtraction: Taking one number away from another to find the difference.
• Multiplication: Adding a number to itself a certain number of times.
• Division: Splitting a number into equal parts.

In finding the distance, understanding subtraction helps us accurately determine how far apart two points are when they lie in the same direction from a common reference point.
Solid knowledge of these basic operations ensures that solving such problems becomes easier and more intuitive for students.