A worker earns 9 dollars per hour for a regular workday and $13.50 per hour for additional hours. if the worker was paid $114.75 for an 11-hour workday, what is the length of a regular workday?

Let us assume that the number of hours of regular work day to be "X". Since the total number of hours worked is 11, the additional hours that the worker put in would be "11-X"

Now, we form the equation to solve for X.

The wage for a regular hours is $9 for X hours worked which would make the pay = 9X

The wage for additional "11-X" hours is $13.50 which would make the pay = (11-X) * 13.50

The total the worker was paid for 11 hours is 114.75, so the equation would be

9X + (11-X) * 13.50 = 114.75

9X + 148.5-13.50X = 11.75

4.5X = 33.75

X = 7.5

So, the length of a regular workday is 7.5 hours