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To solve this problem, we need to define two variables: the number of hours the driver worked and the number of miles the truck drove. Let's break this down step-by-step to write the system of equations.

### Step 1: Define the Variables
- Let $ h $ represent the number of hours the driver worked.
- Let $ m $ represent the number of miles the truck drove.

### Step 2: Analyze the Information Given
1. The driver is paid $20 per hour of driving.
2. Xin incurs a cost of $2.25 per mile driven for gas and maintenance.
3. The total cost for the driver, gas, and maintenance on this particular day is $1457.50.
4. The driver drives at a rate of 50 miles per hour.

### Step 3: Set Up the Equations
1. The cost for the driver, based on the number of hours worked, is $ 20h $ (since the driver earns $20 per hour).
2. The number of miles driven is related to the number of hours worked by the equation $ m = 50h $ (since the truck drove 50 miles per hour).
3. The cost for gas and maintenance is $ 2.25m $.
4. The total expenses are the sum of the driver's pay and the cost of gas and maintenance, which equals $1457.50.

Thus, we can write the system of equations as follows:

1. $ m = 50h $ (this equation links miles driven to hours worked).
2. $ 20h + 2.25m = 1457.50 $ (this equation represents the total cost).

### Final Answer:

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

System of equations:

\[
m = 50h
\]
\[
20h + 2.25m = 1457.50
\]

Would you like further details on how to solve this system, or do you have any questions?

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Here are 5 related questions to think about:
1. How would the system change if the cost per mile for gas and maintenance increased?
2. What if the driver’s hourly wage was different, how would that affect the system?
3. How would you solve this system of equations to find the exact values for $ h $ and $ m $?
4. How can you interpret the meaning of the solution in the context of the business operation?
5. What if the truck drove at a variable speed instead of 50 miles per hour?

**Tip:** In problems like this, always check if the relationship between the variables (hours worked, miles driven) is linear, which simplifies setting up the equations.

Xin owns a trucking company. For every truck that goes out, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 50 miles per hour and Xin's total expenses for the driver, gas, and truck maintenance were $1457.50. 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.

Learn how to write a system of linear equations to determine the number of hours a driver worked and the number of miles driven, based on total expenses for a trucking company. Includes step-by-step breakdown and solution, with key cost analysis.

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