Let's solve this problem step-by-step:
Step 1: Understanding the Problem
The car is reversing, which means it is moving in the negative direction. Initially, the car backs up 24 feet, and then it backs up an additional 12 feet. We want to find the total backward distance the car travels.
Step 2: Represent the Movements with a Drawing
You can draw a simple sketch where the car first moves backward by 24 feet and then by an additional 12 feet. To help visualize this, we can use a number line.
```
|---------|---------|---------|---------|---------|---------|---------|---------|---------|---------|---------|---------|
0 -4 -8 -12 -16 -20 -24 -28 -32 -36 -40 -44 ...
```
- The car starts at position 0.
- It moves to -24 feet.
- Then, it moves 12 feet further back to -36 feet.
Step 3: Represent with an Equation
The positions can also be represented with the equation:
[tex]\[
-24 + (-12)
\][/tex]
Step 4: Calculate the Total Movement
Let's add the two negative numbers together:
[tex]\[
-24 + (-12) = -36
\][/tex]
So the car backs up a total of 36 feet.
Summary
The initial position change is -24 feet. The subsequent position change is -12 feet. Adding these movements together:
[tex]\[
-24 + (-12) = -36
\][/tex]
Thus, the car backs up a total of 36 feet. The position of the car after reversing these distances is at -36 feet.
