The difference between the work rate of three persons and the work rate
of two people, gives the work rate of the third person.
Correct response:
- The number of days it will take Cory to paint the house alone is <u>36 days</u>.
<h3 /><h3>Methods used to obtain Cory's rate of work </h3>
The duration needed for Cory, Amanda, and Bryan together to finish painting the house = 9 days
The duration needed for Amanda and Bryan together to paint the house = 12 days
Required:
The number of days Cory will take to paint the house alone.
Solution:
Let t₁ represent the time it takes Cory to paint the house alone, let t₂
represent the time it takes Amanda to paint the house alone, and let t₃
represent the time it takes for Bryan to paint the house alone.
The work rate formula is presented as follows
![\displaystyle \frac{1}{t} = \mathbf{ \frac{1}{t_1} +\frac{1}{t_2} +\frac{1}{t_3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7Bt%7D%20%20%3D%20%5Cmathbf%7B%20%5Cfrac%7B1%7D%7Bt_1%7D%20%2B%5Cfrac%7B1%7D%7Bt_2%7D%20%2B%5Cfrac%7B1%7D%7Bt_3%7D%7D)
Where;
t = The time it takes to paint the house together = 9 days
Which gives;
![\displaystyle \frac{1}{9} = \frac{1}{t_1} +\frac{1}{t_2} +\frac{1}{t_3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B9%7D%20%3D%20%5Cfrac%7B1%7D%7Bt_1%7D%20%2B%5Cfrac%7B1%7D%7Bt_2%7D%20%2B%5Cfrac%7B1%7D%7Bt_3%7D)
From the question, we have;
The time it takes Amanda and Bryan to paint the house together, is 12 gays, therefore;
![\displaystyle \frac{1}{12} = \mathbf{\frac{1}{t_2} + \frac{1}{t_3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cmathbf%7B%5Cfrac%7B1%7D%7Bt_2%7D%20%2B%20%5Cfrac%7B1%7D%7Bt_3%7D%7D)
![\displaystyle \frac{1}{9} = \frac{1}{t_1} + \frac{1}{12}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B9%7D%20%3D%20%5Cfrac%7B1%7D%7Bt_1%7D%20%20%2B%20%5Cfrac%7B1%7D%7B12%7D)
![\displaystyle \frac{1}{t_1} = \frac{1}{9} -\frac{1}{12} = \mathbf{\frac{1}{36}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7Bt_1%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D%20-%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cmathbf%7B%5Cfrac%7B1%7D%7B36%7D%7D)
- The duration in days it will take Cory to paint the house alone, t₁ = <u>36 days</u>
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