Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2775...

Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2775. What was the rate charged per hour by each mechanic if the sum of the two rates was $220 per hour?

Answer 1

Let the rate of the first mechanic (who works for 10 hours) be x.

Let the rate of the second mechanic (who works for 15 hours) be y.

Equation 1: It is given that the sum of the two rate x and y is $220 per hour. Therefore, our first equation is

x + y = 220

Equation 2: Cost of first mechanic is 10x and the cost of the second mechanic is 15y and it is given that the total cost for both is $2,775. Therefore, our second equation is

10x + 15y = 2775

We solve by the method of substitution. Solving equation 1 for y, we get

y = 220 - x

Now plugging this value of y in equation 2, we get

10x + 15(220 - x) = 2775

10x + 3300 - 15x = 2775

- 5x = - 525

x = 105

Plugging this back in y = 220 - x, we see that y = 220 - 105 = 115.

Therefore, the first mechanic charges $105/hr and the second mechanic charge $115/hr.