Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1400. what was the rate charged per hour by mechanic if the sum of the two rates was $130 per hour

Let's define variables:
 x = Rate in $ / hr of the mechanic working 15hr
 y = Rate in $ / hr of the mechanic working 5hr
 We have the following system of equations:
 x + y = 130
 15x + 5y = 1400
 Solving the system we have:
 x = $ 75 / hr
 y = $ 55 / hr
 
 the rate charged per hour by mechanics was:
 x = $ 75 / hr
 y = $ 55 / hr