Allison owns a trucking company. For every truck that goes out, Allison must pay the driver $11 per hour of driving and also has an expense of $1 per mile
driven for gas and maintenance. On one particular day, the driver drove an
average of 15 miles per hour and Allison's total expenses for the driver, gas
and truck maintenance were $286. 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.

y = 15x

11x + y = 286

where

y = number of miles driven by the truck driver

x = number of hours the truck driver drives

Solving this gives, x = 11 hours and y = 165 miles.

Step-by-step explanation:

Let the number of hours the truck driver drives be x.

Let the number of miles driven by the truck driver be y.

Since the truck driver drives at 15 miles per hour, the number of miles covered by the driver y, can be given from the speed equation.

Speed = (distance/time)

15 = (y/x)

y = 15x.

And the drivers are paid $11 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance.

Meaning that on a day that the truck driver drives y miles for x hours, the total pay, C, is given as

C = 11x + 1y = 11x + y

So, on this fateful day, the total amount paid to a truck driver was $286

So, C = $286

11x + y = 286.

So, the two equations for the scenarios are

y = 15x

11x + y = 286

Solving this gives, x = 11 hours and y = 165 miles.