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To set up the system of equations for this problem, let's define the variables:

1. **Let $ h $** = number of hours the driver worked.
2. **Let $ m $** = number of miles the truck drove.

Now, based on the information given:

- The driver earns **$16 per hour**. Therefore, the total pay for the driver would be $ 16h $.
- The truck incurs an additional **$1.25 per mile** driven, covering gas and maintenance costs. So, the cost for gas and maintenance would be $ 1.25m $.
- We know that on that day, the driver drove **20 miles per hour**. This provides a relationship between hours and miles: $ m = 20h $.
- The total expense was **$205**, which includes both the driver’s wages and the gas/maintenance costs. So, we have $ 16h + 1.25m = 205 $.

### System of Equations
Using the information above, we can set up the following system:

1. $ m = 20h $
2. $ 16h + 1.25m = 205 $

This system of equations can now be used to solve for $ h $ and $ m $.

Would you like further details on solving this system?

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**Relative Questions to Explore Further:**

1. How can we solve the system of equations using substitution?
2. What would happen to the total cost if the mileage cost increased?
3. How does the driving rate of 20 miles per hour affect the total expenses?
4. What if the hourly rate for the driver changes—how would that impact the equations?
5. Can this system of equations be graphed to visualize the solution?

**Tip:** When defining variables, choose letters that are meaningful to help you remember their purpose in the problem!

Logan owns a trucking company. For every truck that goes out, Logan must pay the driver $16 per hour of driving and also has an expense of $1.25 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 20 miles per hour and Logan's total expenses for the driver, gas, and truck maintenance were $205. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.

Learn how to set up and solve a system of equations to determine driving hours and mileage for a trucking company with costs for driver wages and gas. Suitable for Grades 8-10.

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