Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1,800. What was the rate charged per hour by each mechanic of the sum of the two rates was $105 per hour?

Let the first mechanic's rate per hour be x, and the second mechanic's rate per hour be y. We know that the first mechanic worked for 20 hours, so he earned 20x dollars. Similarly, the second mechanic earned 15y dollars. Together, they earned a total of 1800 dollars. So we can write an equation: 20x + 15y = 1800 We also know that the sum of their rates is 105 dollars per hour. So we can write another equation: x + y = 105 Now we have two equations with two unknowns. We can solve for x and y by using substitution or elimination. Here we'll use substitution: From the second equation, we can solve for y: y = 105 - x Now we substitute this expression for y into the first equation: 20x + 15(105 - x) = 1800 Simplifying: 20x + 1575 - 15x = 1800 5x = 225 x = 45 So the first mechanic charged 45 dollars per hour, and the second mechanic charged: y = 105 - x = 60 dollars per hour. Therefore, our final answer is that the first mechanic charged $45 per hour and the second mechanic charged $60 per hour.