We need to create two expressions, then equate them in order to find the numbers of hours.
Let X = Number of hours
Let 1200+18x = Company A (Flat Fee + Hourly Rate*Hours)
Let 900+23x = Company B
[tex]1200+18x=900+23x\\300+18x=23x\\300=5x\\60=x[/tex]
After 60 hours, the prices will be the same