Question

an auto shop has two mechanics. they charge a combined rate of $185 per hour. on their most recent car, the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of $1400.
what is the rate charged per hour by each mechanic?
first mechanic: $ per hour
second mechanic: $ per hour

Explanation:

Step1: Set up equations

Let the rate of the first mechanic be \(x\) dollars per hour and the rate of the second mechanic be \(y\) dollars per hour. We know that \(x + y=185\) (combined rate) and \(10x + 5y = 1400\) (total charge).

Step2: Substitute \(y = 185 - x\) into the second equation

Substitute \(y\) into \(10x + 5y=1400\), we get \(10x+5(185 - x)=1400\).
Expand: \(10x + 925-5x=1400\).
Combine like - terms: \(5x=1400 - 925\).
So, \(5x = 475\).
Solve for \(x\): \(x=\frac{475}{5}=95\).

Step3: Find \(y\)

Since \(x + y=185\) and \(x = 95\), then \(y=185 - 95 = 90\).

Answer:

First mechanic: \(\$95\) per hour, Second mechanic: \(\$90\) per hour.