Two mechanics worked on a car problem.

Question

Two mechanics worked on a car. The first mechanic worked for 20

 hours, and the second mechanic worked for 5

 hours. Together they charged a total of $1725

.What was the rate charged per hour by each mechanic if the sum of the two rates was $150

 per hour? 

Answer 1

If we let x represent the hourly of the first mechanic and y represent the hourly rate of the second mechanic, then we can write the following equation to show the total earned by the two:

20x + 5y = 1725

We can also write the following equation to represent the sum of the rates:

x + y =150

Using these two equations , we can determine each of their rates.

Using the second equation , we can say that y = 150 - x

We can substitute this expression for y into our first equation: 20x + 5 (150 - x) = 1725

Combing like terms and using the distributive property with inverse operations gives us:

20x + 750 -5x = 1725

15x + 750 = 1725

15x+ 750 -750 = 1725 - 750

15x = 975

15x/15 = 975/15

x = $65 per hour for the first mechanic

y will be $85 per hour for the second mechanic because 65 + 85 = 150