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 $2075 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour?

If the first mechanic charged x dollars per hour and the second charged y dollars per hour, we have x+y=160 and 10x+15y=2075 due to that we add x or y for every hour spent.

x+y=160
10x+15y=2075
Multiplying the first equation by -10 and adding it to the second, we get 5y=2075-1600=475. Dividing both sides by 5, we get y=95. For the first mechanic, we can plug 95 for y into the first equation to get x+95=160. Next, we can subtract 95 from both sides to get x=65