two mechanics worked on a car. The first mechanic worked for 10 hrs, and the second mechanic worked for 5 hours. Together they charged a total of $1475. What was the rate charged per hour by mechanic if the sum of the two rates was $190 per hour? What is the first mechanic make per hour? And what did the second mechanic make per hour?

Lets start off by letting x be the first mechanics rate and y being the second mechanics rate. We know that the first mechanic worked 5 hours and that the second mechanic worked 10 hours and together they charged 1150. An equation to express this would be:

5x+10y = 1150

We also know that together they charged 160/per hour. An equation to express this would be:

x+y = 160

Now we can solve the second equation for x or the first mechanics rate.

x+y = 160

x = 160 - y

Now that we have an expression for x we can plug that back into the first equation and solve for y or how much the second mechanic charged.

5x+10y=1150 plug in x =160-y

5(160-y)+10y=1150 Distribute

800 -5y+10y = 1150 Combine like terms

800 +5y = 1150 Subtract 800 from both sides

5y = 350 divide by 5

y = 70

So we know that the second mechanic charged $70/hour. We also know that(from our work before) that the first mechanic charges $160 - the rate the second mechanic charged. We know that's $70/hour so we can plug in and solve for the first rate.

x = 160-y

x = 160-70

x = 90

So we know that the first mechanic charged $90/hour and the second mechanic charged $70/hour.