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.

Let's define the variables first:

- Let **$ h $** represent the number of hours the driver worked.
- Let **$ m $** represent the number of miles the truck drove.

Given this setup, we have two pieces of information:

1. **Driver's Wage**: Logan pays the driver $16 per hour. So, the total payment for the driver is $ 16h $.
2. **Expenses for Gas and Maintenance**: Logan incurs an expense of $1.25 per mile. Therefore, the total expense for gas and maintenance is $ 1.25m $.

Additionally, it's given that the driver drove at an average speed of 20 miles per hour, which can be represented by the equation:

\[
m = 20h
\]

The total expenses (including both the driver's wage and the gas/maintenance costs) amount to $205. This can be expressed as:

\[
16h + 1.25m = 205
\]

### System of Equations:
\[
\begin{aligned}
1. & \quad m = 20h \\
2. & \quad 16h + 1.25m = 205
\end{aligned}
\]

This system of equations can be used to determine the values of $ h $ (the number of hours worked) and $ m $ (the number of miles driven).

Would you like to solve this system of equations or do you have any questions about the setup?

Here are 5 related questions to expand on this problem:

1. How would the system change if the driver’s wage was $18 per hour instead of $16?
2. What would happen to the system of equations if the gas and maintenance cost increased to $1.50 per mile?
3. How many hours would the driver have worked if the total expenses were $220 instead of $205?
4. What if the average speed was 25 miles per hour? How would the system of equations change?
5. How can you solve this system of equations using the substitution method?

**Tip:** When defining variables in word problems, clearly associating each variable with a specific quantity helps in forming accurate equations.

Understand how to determine the number of hours a driver worked and the miles driven by a truck using a system of equations. Explore the solution step-by-step, including variables for driver wages and gas expenses. Suitable for high school students and above.

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