I’m having trouble understanding this question. Specifically, how does it imply that $240 is a fixed payment for the job? In the second equation, where the number of hours is reduced by 2 and the hourly rate increases by $6, Greg sets the total equal to $240.
Here’s how I’ve defined the variables:
Let x represent the hourly wage rate.
Let n represent the number of hours worked.
The equations given are:
xn=240
(x+6)(n−2)=y (y being the new total payment)
Why would y be equal to $240? The question never states that the total payment is fixed. Could you please clarify this?
Initially, he thought the work would take t hours, but he actually finished it in t- 2 hours. According to the question, the contractor charged $240 (fixed cuz the client already paid) despite how long he actually took to complete it (“resulting in … increase in his per hour rate”).
His hourly rate initially was \frac{240}{t} and later it was \frac{240}{t-2}. It’s clear that the hourly rate has increased, but by how much? “hourly rate increases by 6”
