Question

an auto shop has two mechanics. they charge a combined rate of $175 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 $3150. what is the rate charged per hour by each mechanic? first mechanic: $ per hour second mechanic: $ per hour

Explanation:

Step1: Define variables

Let \( x \) be the rate of the first mechanic (in dollars per hour) and \( y \) be the rate of the second mechanic (in dollars per hour). We know that their combined rate is \( \$175 \) per hour, so we have the equation \( x + y = 175 \). Also, the first mechanic worked 20 hours and the second worked 15 hours, with a total charge of \( \$3150 \). So the second equation is \( 20x + 15y = 3150 \).

Step2: Solve the system of equations

From the first equation, we can express \( y \) in terms of \( x \): \( y = 175 - x \). Substitute this into the second equation:

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Step3: Find \( y \)

Now substitute \( x = 105 \) back into \( y = 175 - x \):
\( y = 175 - 105 = 70 \)

Answer:

First mechanic: $105 per hour
Second mechanic: $70 per hour