Question

an auto shop has two mechanics. they charge a combined rate of $110 per hour. on their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $1875. what is the rate charged per hour by each mechanic? first mechanic: $ per hour second mechanic: $ per hour

Explanation:

Step1: Define variables for rates

Let $x$ = first mechanic's rate (\$/hr), $y$ = second mechanic's rate (\$/hr)

Step2: Set up system of equations

1. Combined rate: $x + y = 110$
2. Total earnings: $20x + 15y = 1875$

Step3: Simplify total earnings equation

Divide second equation by 5: $4x + 3y = 375$

Step4: Solve for one variable

From first equation: $y = 110 - x$. Substitute into simplified equation:
$4x + 3(110 - x) = 375$

Step5: Calculate first mechanic's rate

Expand and solve:
$4x + 330 - 3x = 375$
$x = 375 - 330 = 45$

Step6: Calculate second mechanic's rate

Substitute $x=45$ into $y=110-x$:
$y = 110 - 45 = 65$

Answer:

First mechanic: $\$45$ per hour
Second mechanic: $\$65$ per hour