Quick Fix Inc. repairs bikes. The company’s revenue is modeled by the function R(h)=220h−160 for every h hours spent repairing bikes. The company’s overhead cost is modeled by the function C(h)=20h2−400 . After how many hours does the company break even? Enter your answer in the box.

The company will break even after 12 hours.

To find this answer, we have to set the equations equal to each other and solve. We will have a quadratic equation.

[tex]20x^2-400=220h-160 [/tex]

This can simplify to:
[tex]x^2 - 11h - 12 = 0[/tex]

The factors of this are: (x - 12) and (x + 1).

The only reasonable solution is 12 hours.