Two mechanics worked on a car. the first mechanic charged $45 per hour, and the second mechanic charged $55 per hour. the mechanics worked for a
combined total of 25 hours, and together they charged a total of $1175. how long did each mechanic work?

Let first mechanic worked for X and second be Y.

So, X + Y = 25
X = 25-Y

And total they charged-
45X + 55Y = 1175
5 (9X + 11Y) = 235 * 5
(9X + 11Y) = 235
11Y = 235-9X

From fist statement: X=25-Y

11Y = 235-9(25-Y)
11Y = 235-225+9Y
11Y = 10+9Y
11Y - 9Y = 10
2Y = 10
Y= 10/2
Y=5 hours

X=25-Y
X=25-5
X=20

X worked for 20 hours and Y for 5 hours.

PS. Moral of the story- You can say Y was lazy but still charged more than Y. Just kidding!