Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $80 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1975. How long did each mechanic work?
Let x be the number of hours the first mechanic worked.
The first mechanic earned 105x dollars.
The second mechanic worked for 20 - x hours.
The second mechanic earned 80(20 - x) dollars.
105x + 80(20 - x) = 1975
105x + 1600 - 80x = 1975
25x = 375
x = 15
The first mechanic worked for 15 hours, and the second mechanic worked for 20 - 15 = <<20-15=5>>5 hours. Answer: \boxed{15}.
Let's assume that the first mechanic worked for "x" hours and the second mechanic worked for "y" hours.
Given that the first mechanic charged $105 per hour, the total cost of his work can be represented as 105x.
Similarly, the second mechanic charged $80 per hour, so the total cost of his work can be represented as 80y.
We also know that the mechanics worked for a combined total of 20 hours, so x + y = 20.
And together, they charged a total of $1975, so 105x + 80y = 1975.
Now, we can solve these two equations simultaneously to find the values of x and y.
Using the first equation, we can rewrite it as y = 20 - x.
Substituting this value into the second equation, we have 105x + 80(20 - x) = 1975.
Simplifying, we get 105x + 1600 - 80x = 1975.
Combining like terms, we have 25x = 375.
Dividing both sides by 25, we find x = 15.
By substituting this value back into x + y = 20, we find that y = 5.
Therefore, the first mechanic worked for 15 hours, while the second mechanic worked for 5 hours.