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# Pay per hour in a week. (differential equations question, kind of) watch

1. So let's say we have two (or more) people working on a project. 'S' pounds per hour is allocated for them each week, example: let's say for week 'w' , 5 pounds per hour (pph) was allocated, so hourly rate of person 1 + person 2 + ...=5 pph in that week.
So let the hours worked by person 'n' in that week be , and the amount of money earned by that person be ; therefore, the hourly rate must be .
Now I want the hourly rate of the person to be equal to , ie.

This should agree with my initial statement that:

The problem is that I want to find 'P', but when I do that I get something weird, which makes me think that my whole approach is wrong.
So what I'm asking is, does this make sense?
2. bump
3. Bump 2
4. (Original post by gagafacea1)
...
It's very difficult to follow what's going on here.

So let's say we have two (or more) people working on a project. 'S' pounds per hour is allocated for them each week, example: let's say for week 'w' , 5 pounds per hour (pph) was allocated, so wage of person 1 + person 2 + ...=5 pph in that week.[./quote]

If it's S pounds per week, why choose a particular week? Does S depend on w?

So let the hours worked by person 'n' in that week be , and the amount of money earned by that person be ; therefore, the wage must be .
What's "d" - I hope it's not the derivative.

If the wage is S, then S=P(n)/T(n) for all n. When you say wage, you seem to mean wage/hour.

Now I want the wage of the person to be equal to , ie.
But you've initially set the wage to S.

This should agree with my initial statement that:

The problem is that I want to find 'P', but when I do that I get something weird, which makes me think that my whole approach is wrong.
So what I'm asking is, does this make sense?
Sorry, does my head in just reading this - can't figure out what you're doing.
5. (Original post by ghostwalker)
It's very difficult to follow what's going on here.

Sorry, does my head in just reading this - can't figure out what you're doing.
Yeah I meant hourly rate sorry, but why wouldn't the hourly rate be the derivative of wage with respect to hours worked?
6. (Original post by gagafacea1)
Yeah I meant hourly rate sorry, but why wouldn't the hourly rate be the derivative of wage with respect to hours worked?
I did say it was difficult to follow. It seems redundant if S=P(n)/T(n) - you've not said that was incorrect.
7. (Original post by ghostwalker)
I did say it was difficult to follow. It seems redundant if S=P(n)/T(n) - you've not said that was incorrect.
I'm really sorry, I didn't intend it to be that confusing at all, it seemed very straight forward to me.
S is the sum of all the wage/hour of the workers, S is a constant (kind of), but that's not important. What's important is the fact that the hourly wage of a person is NOT constant, it is directly proportional to
(number of hours worked by person)/(number of hours worked by everyone)
Is that clear enough?
8. (Original post by gagafacea1)
I'm really sorry, I didn't intend it to be that confusing at all, it seemed very straight forward to me.
S is the sum of all the wage/hour of the workers, S is a constant (kind of), but that's not important. What's important is the fact that the hourly wage of a person is NOT constant, it is directly proportional to
(number of hours worked by person)/(number of hours worked by everyone)
Is that clear enough?
Surely the hourly wage is constant? Their daily pay would be directly proportional to the hours worked.

Or are you saying that the employee's hourly pay is calculated using the ratio of their hours worked to the total hours worked by everyone? This seems strange.
9. (Original post by lizard54142)
Surely the hourly wage is constant? Their daily pay would be directly proportional to the hours worked.

Or are you saying that the employee's hourly pay is calculated using the ratio of their hours worked to the total hours worked by everyone? This seems strange.
Exactly that! I know it is strange, but I want it to be like that.
10. (Original post by gagafacea1)
Exactly that! I know it is strange, but I want it to be like that.
What is this, is it a project you're working on or is it a particular question?

(Original post by gagafacea1)
So let's say we have two (or more) people working on a project. 'S' pounds per hour is allocated for them each week, example: let's say for week 'w' , 5 pounds per hour (pph) was allocated, so wage of person 1 + person 2 + ...=5 pph in that week.
So let the hours worked by person 'n' in that week be , and the amount of money earned by that person be ; therefore, the wage must be .
Now I want the wage of the person to be equal to , ie.

This should agree with my initial statement that:

The problem is that I want to find 'P', but when I do that I get something weird, which makes me think that my whole approach is wrong.
So what I'm asking is, does this make sense?
Does everyone have the same hourly rate? If so shouldn't the bit in bold be:

"person 1 = person 2 = ...=5 pph in that week"?
11. (Original post by lizard54142)
What is this, is it a project you're working on or is it a particular question?

Does everyone have the same hourly rate? If so shouldn't the bit in bold be:

"person 1 = person 2 = ...=5 pph in that week"?
Just something I was thinking about, neither a project nor a particular question (like not an exam question).
But it's not, because the number of ours they've worked might be different, example:
There are two people working on this project:
In week 1, person1 worked 4 hours, person2 worked 5 hours.
Then, the hourly wage of person1 in that week is proportional to 4/(4+5)=4/9.
While for person2, it's 5/(4+5)=5/9
I'm honestly struggling to see why this is very confusing, I know it's made up, but like, I don't know, I'm sorry.
12. (Original post by gagafacea1)
Just something I was thinking about, neither a project nor a particular question (like not an exam question).
But it's not, because the number of ours they've worked might be different, example:
There are two people working on this project:
In week 1, person1 worked 4 hours, person2 worked 5 hours.
Then, the hourly wage of person1 in that week is proportional to 4/(4+5)=4/9.
While for person2, it's 5/(4+5)=5/9
I'm honestly struggling to see why this is very confusing, I know it's made up, but like, I don't know, I'm sorry.
Ah okay, I follow that. What is the total amount of money put aside for wages each week, S? So for person one:

total pay for week = S * (4/9)?
13. (Original post by lizard54142)
Ah okay, I follow that. What is the total amount of money put aside for wages each week, S? So for person one:

total pay for week = S * (4/9)?
Nope, S is the total amount for hourly wage:

hourly wage= S*(4/9)

I can see where you're getting confused, I've always thought wage=hourly rate, since english is my second language and we use the same word for both things in Iraqi so I'm sorry about that.
14. (Original post by gagafacea1)
Nope, S is the total amount for hourly wage:

hourly wage= S*(4/9)

I can see where you're getting confused, I've always thought wage=hourly rate, since english is my second language and we use the same word for both things in Iraqi so I'm sorry about that.
So surely if there's a lot of employees (say 100), they would get paid next to nothing, as their fraction of the total hours worked would be tiny.
15. (Original post by lizard54142)
So surely if there's a lot of employees (say 100), they would get paid next to nothing, as their fraction of the total hours worked would be tiny.
Yup, I don't really care about their feelings lol. No but in that case I would increase S! maybe even make S a function of the total number of hours worked by all employees. My problem is with the fact that the derivative of wage with respect to number of hours worked SHOULD be equal to the hourly rate, but it doesn't make sense when you try to find a solution for the wage as a function of number of hours worked.
16. (Original post by gagafacea1)
Yup, I don't really care about their feelings lol. No but in that case I would increase S! maybe even make S a function of the total number of hours worked by all employees. My problem is with the fact that the derivative of wage with respect to number of hours worked SHOULD be equal to the hourly rate, but it doesn't make sense when you try to find a solution for the wage as a function of number of hours worked.
Going back to your initial post, I don't think you can model hourly rate as a differential equation? Why would it be (change in money earnt)/(change in time worked)? Surely it is just (money earnt)/(time worked)?
17. (Original post by lizard54142)
Going back to your initial post, I don't think you can model hourly rate as a differential equation? Why would it be (change in money earnt)/(change in time worked)? Surely it is just (money earnt)/(time worked)?
You know what, I think you're right. It's probably that simplistic view of the velocity-displacement equation that got me. So you think it should be:
P(n)/T(n)=T(n)/sumT * S
ie. P(n)=T(n)^2/sumT * S
I've always thought that rate=derivative, by maybe it has to be 'rate of change = derivative'.
18. (Original post by gagafacea1)
You know what, I think you're right. It's probably that simplistic view of the velocity-displacement equation that got me. So you think it should be:
P(n)/T(n)=T(n)/sumT * S
ie. P(n)=T(n)^2/sumT * S
I've always thought that rate=derivative, by maybe it has to be 'rate of change = derivative'.
The definition of a derivative is the sensitivity of a system/function/model to change. Yes, your new equations looks better.

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