MHB Rational Expression word problem

[Pikachu1]

Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to maintain a lawn is approximately 0.05A + 0.25.

Write a rational expression for nancy profit per hour.
Evaluate the expression for a yard with an area of 90m^2Obviously there is some sort of formula for this that i don't understand.

 

[MarkFL]

When you see the word "per" (which means "for each"), as in miles per hour (or profit per hour), this means you want to take some total and divide by the number of hours. You are given both the total profit, and the number of hours, both as a function of $A$. Can you now construct a profit per hour function $P_h$ for Nancy?

$$P_h(A)=\frac{\text{Total profit}}{\text{hours to maintain a lawn}}=?$$

 

[Pikachu1]

When you see the word "per" (which means "for each"), as in miles per hour (or profit per hour), this means you want to take some total and divide by the number of hours. You are given both the total profit, and the number of hours, both as a function of $A$. Can you now construct a profit per hour function $P_h$ for Nancy?

$$P_h(A)=\frac{\text{Total profit}}{\text{hours to maintain a lawn}}=?$$

So it would be,

Ph(A) =$5A/ 0.05A + 0.25 ?

I feel like i am still missing something.

 

[MarkFL]

So it would be,

Ph(A) =$5A/ 0.05A + 0.25 ?

I feel like i am still missing something.

I would just recognize that the units of the function are dollars per hour, and if using plain text, use bracketing symbols to indicate clearly what the denominator is as follows:

P_h(A) = 5A/(0.05A + 0.25)

So, for part b), you need to evaluate P_h(90). :D

 

[Pikachu1]

I would just recognize that the units of the function are dollars per hour, and if using plain text, use bracketing symbols to indicate clearly what the denominator is as follows:

P_h(A) = 5A/(0.05A + 0.25)

So, for part b), you need to evaluate P_h(90). :D

So, it would be? I have no idea why this question stomped me like that.
P_h(90) = 5(90)/0.05(90) +0.25 ?

 

[MarkFL]

So, it would be? I have no idea why this question stomped me like that.
P_h(90) = 5(90)/0.05(90) +0.25 ?

Well, you really need bracketing symbols...

P_h(90) = 5(90)/(0.05(90) + 0.25)

The way you write it means:

$$P_h(90)=\frac{5(90)}{0.05(90)}+0.25$$

But what you want is:

$$P_h(90)=\frac{5(90)}{0.05(90)+0.25}$$

And the parentheses makes the meaning clear. :D

 

[Pikachu1]

Well, you really need bracketing symbols...

P_h(90) = 5(90)/(0.05(90) + 0.25)

The way you write it means:

$$P_h(90)=\frac{5(90)}{0.05(90)}+0.25$$

But what you want is:

$$P_h(90)=\frac{5(90)}{0.05(90)+0.25}$$

And the parentheses makes the meaning clear. :D

Thank you! I understand now.
You rock