I feel bad I can't understand the most simple of algebra

[Ouabache]

P = (r1 * t1) + (r2 * t2)

$550 = (10/per hour * 40) + ($15 per hour * 10)

As Mark44 mentioned, we are looking for an expression(s), not specific values.
Yes we could have 2 equations with condition on each.
This is actually very useful for the general case, where work is anywhere from 1hr up to some large number.

For your original question:

Calculate your pay if you work more than 40 hours and are paid time and one half for every hour past 40.

for example:
P - pay ($)
r - normal rate of pay ($/hr)
t - time worked (hr)

equ. (1) P = r * t ; amount of pay working < or = 40 hrs
equ. (2) P = (3/2)r * t; amount pay for "only" time worked > 40hrs
Total Pay is sum of equ. (1) and (2)

For your example, we are given the person is working more than 40 hrs.
I suggested we could write this in a combined expression of the form:

equ. (3) P = (r1 * t1) + (r2 * t2)

here are the values I was hoping you would determine from our disussion:
r1 = r (the normal pay rate)
t1 = 40 (maximum normal number of hours)
r2 = (3/2) * r (time and a half; one and half times normal rate)
t2 = t-40 (the number of hours over 40 that have been worked)

Substituting those terms into the combined equation (3)
and you have valid solution to this problem, written in terms of the original r and t.

 

[Mark44]

Ahh, I see. I was supposed to write it in algebra format.

That makes sense

Let's say p = $550, then
P= 10*(40) + 15(the overtime rate)*10

To get the overtime rate multiply 1.5 x 10 (the normal rate)

No, let's not say that P = $550. You are starting with what you assume to be the answer, and as I said before, your answer will not be a specific number.

If the employee works H hours at $10/hour, what is the employee's gross pay?

You need to take into account whether the employee worked overtime hours, and your two formulas should produce algebraic expressions, not numbers, that reflect two situations.