Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1800. What was the rate charged per hour by each mechanic if the sum of the two rates was $190 per hour?
The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.
To solve this problem, we'll assign variables to represent the rates charged by each mechanic. Let's call the rate of the first mechanic "x" dollars per hour, and the rate of the second mechanic "y" dollars per hour.
We know that the sum of the two rates is $190 per hour, so we can write the equation:
x + y = 190 ---- (Equation 1)
We also know that the first mechanic worked for 15 hours and the second mechanic worked for 5 hours, and together they charged a total of $1800. To find the total amount charged by each mechanic, we multiply their respective rates by the number of hours they worked and sum them up:
15x + 5y = 1800 ---- (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
To do this, we can use one of several methods, such as substitution or elimination. Let's use the substitution method here.
Rearrange Equation 1 to solve for x:
x = 190 - y
Now, substitute this expression for x in Equation 2:
15(190 - y) + 5y = 1800
Multiplying, we get:
2850 - 15y + 5y = 1800
Combining like terms:
-10y = 1800 - 2850
Simplifying:
-10y = -1050
Divide both sides by -10:
y = 105
Substitute this value of y back into Equation 1 to find x:
x + 105 = 190
Subtract 105 from both sides:
x = 190 - 105
x = 85
Therefore, the rate charged by the first mechanic is $85 per hour, and the rate charged by the second mechanic is $105 per hour.