Two mechanics worked on a car

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 $1400. What was the rate charged per hour by each mechanic if the sum of the two rates was $115 per hour?

First mechanic:

Second mechanic:

Answer 1

This type of problem works as a system of equations.

First we name our two mechanics: Mechanic 1 will be X, Mechanic 2 will by Y

Let's find our information in the problem:

Mechanic X worked 10 hours

Mechanic Y worked for 15 hours.

Together they charged $1400

The hourly rate for both mechanics was $115.

Making our first equation:

10X+15Y=1400

Our second equation would be:

X+Y=115

Now you can use any method to solve the system. I would choose substitution because that will be the easiest in my mind. (you can do graphing or elimination, if you would like.)

Change the second equation to: X=115-Y and then put into the first equation to replace the X.

10(115-Y)+15Y=1400

1150-10Y+15Y=1400 (multiply the first part of the equation.)

1150+5Y=1400 (Combine like terms)

1150-1150+5Y=1400-1150 (isolate the variable by eliminating the constant on both sides to keep equation balanced)

5Y=250 (simplify)

Y=50 (divide both sides by 5 to isolate the variable)

Now substitute back into the second equation:

X=115-50

X=65

You can check the problem by replacing the variables in the first equation with the solutions you found and make sure that the final answer is correct.

Answer 2

Answered above.