Question

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

Answer 1

X - the rate charged by the first mechanic
y - the rate charged by the second mechanic

The sum of the two rates was $155.
$x+y=155 \\ y=155-x$

The first mechanic worked for 10 hours, the second mechanic worked for 5 hours, and together they charged $1000.
$10x+5y=1000 \ \ |\div 5 \\ 2x+y=200 \\ y=200-2x$

Set 155-x and 200-2x equal to each other:
$155-x=200-2x \\ -x+2x=200-155 \\ x=45 \\ \\ y=155-x=155-45=110$

The rate charged by the first mechanic was $45, and the rate charged by the second mechanic was $110.