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Let's break down the problem and solve it step by step.

### Problem:
- The company needs to make **32.9 km** of cable.
- The machine produces **4.5 km** of cable per hour.
- While working, the customer adds **8 km** more to the order.

We are asked to find the equation that models how long it will take to produce all the cable.

### Steps:
1. **Total cable required**: The original order is 32.9 km, but since the customer adds 8 km more, the total length becomes:
   \[
   32.9 + 8 = 40.9 \text{ km}
   \]

2. **Rate of production**: The machine makes cable at **4.5 km per hour**.

3. **Time to produce all the cable**: If we let \(x\) represent the time (in hours), the total cable produced is the rate (4.5 km/h) multiplied by the time, i.e. \(4.5x\).

4. **Set up the equation**: The total amount of cable produced must equal the total cable required:
   \[
   4.5x = 40.9
   \]

Thus, the correct equation is:
\[
\boxed{D: 32.9 + 8 = 4.5x}
\]

### Explanation:
- The left-hand side represents the total length of cable required (32.9 + 8 km).
- The right-hand side represents the total amount of cable produced in \(x\) hours at the rate of 4.5 km/h.

Would you like further details or have any questions?

### Related Questions:
1. How would the equation change if the machine worked faster or slower?
2. How many hours would it take to produce all the cable?
3. What if the customer added more than 8 km to the order—how would the equation change?
4. What is the total time to produce just the original 32.9 km of cable?
5. How can you verify if the equation is correct by plugging in values for \(x\)?

**Tip**: When dealing with rates, always identify the total work required and the rate of work to set up the correct equation.

A company needs to make 32.9 km of cable for a customer. The machine making the cable can create 4.5 km of cable per hour. While the company is working on the cable, the customer adds 8 km to the order. Which equation could be used to find how much time it will take to make all the cable?

Learn how to calculate the time it takes to produce a total of 40.9 km of cable with a machine that produces cable at 4.5 km per hour. This problem uses algebraic equations and rates of work, suitable for Grades 6-8.

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