Question

Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $90 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $1750. How long did each mechanic work?

Answer 1

First mechanic worked 20 hours and second mechanic worked 5 hours

Explanation:

Let the number of hours the first mechanic worked =
`a`

Let the number of hours the second mechanic worked =
`b`

Therefore, we can write 2 equations and then solve them simultaneously:

`a+b=25`

`65a+90b=1750`

Rearranging the first equation:
`a=25-b`

and substituting into the second equation to find
`b`:

`65(25-b)+90b=1750`

`1625-65b+90b=1750\\ 25b=125\\ b=5`

Now sub
`b=5` into the first equation to find
`a`

`a+5=25\\ a=20`

Therefore, first mechanic (a) worked 20 hours and second mechanic (b) worked 5 hours