SOLUTION: Tina and Cal can spray an orchard in 8 hours. Gina , working alone, would take 12 hours to do the job. How long would it take Cal working alone?

Question 110413: Tina and Cal can spray an orchard in 8 hours. Gina , working alone, would take 12 hours to do the job. How long would it take Cal working alone?
Found 2 solutions by solver91311, ptaylor:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First I have to assume that Tina and Gina are the same person, otherwise this problem has no unique solution, and I'm going to call her Tina.
:
Tina working alone could spray the orchard in 12 hours, so that means that Tina can spray orchards per hour.
:
Tina and Cal, therefore, spray orchards per hour together.
:
And finally, Cal can spray orchards per hour by himself.
:

:
The lowest common denominator for these three fractions is 24x, so:
:

:
So Cal would take 24 hours to do the job by himself.

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x= amount of time it takes Cal working alone
Now we know that Gina sprays the orchard at the rate of 1/12 orchard per hour, right?
Both working together sprays the orchard at the rate of 1/8 orchard per hour
And we know that Cal sprays the orchard at 1/x orchard per hour. So our equation to solve is:
(1/12)+(1/x)=(1/8) multiply each term by 24x to get rid of fractions
2x+24=3x subtract 2x from both sides
2x-2x+24=3x-2x collect like terms
24=x or
x=24 hrs----------------------amount of time for Cal working alone
CK
(1/12)+(1/24)=1/8
(2/24)+(1/24)=1/8
3/24=1/8
1/8=1/8

Hope this helps---ptaylor

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