Respuesta :
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 36 days.
Methods used to obtain Cory's rate of work
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
[tex]\displaystyle \frac{1}{t} = \mathbf{ \frac{1}{t_1} +\frac{1}{t_2} +\frac{1}{t_3}}[/tex]
Where;
t = The time it takes to paint the house together = 9 days
Which gives;
[tex]\displaystyle \frac{1}{9} = \frac{1}{t_1} +\frac{1}{t_2} +\frac{1}{t_3}[/tex]
From the question, we have;
The time it takes Amanda and Bryan to paint the house together, is 12 gays, therefore;
[tex]\displaystyle \frac{1}{12} = \mathbf{\frac{1}{t_2} + \frac{1}{t_3}}[/tex]
[tex]\displaystyle \frac{1}{9} = \frac{1}{t_1} + \frac{1}{12}[/tex]
[tex]\displaystyle \frac{1}{t_1} = \frac{1}{9} -\frac{1}{12} = \mathbf{\frac{1}{36}}[/tex]
- The duration in days it will take Cory to paint the house alone, t₁ = 36 days
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