SOLUTION: Hayden is the manager of a landscaping company. He had three employees to do the entire park, Cody Kaitlin and Joseph.Cody can complete the job in 8 hrs. kaitlin can complete th

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hayden is the manager of a landscaping company. He had three employees to do the entire park, Cody Kaitlin and Joseph.Cody can complete the job in 8 hrs. kaitlin can complete th      Log On


   

Question 824509: Hayden is the manager of a landscaping company. He had three employees to do the entire park, Cody Kaitlin and Joseph.Cody can complete the job in 8 hrs. kaitlin can complete the project in 6 hours. Joseph is neew so no one knows how it will take him. They must all work together to complete the project. How could I explain to Hayden how long it would take Joseph working by himself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you add their rates of working, you
will get their rate of working together
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Cody's rate is ( 1 job ) / ( 8 hrs )
Kaitlin's rate is ( 1 job ) / ( 6 hrs )
Let Joseph's rate = ( 1 job ) / ( t hrs )
Let their rate working together = ( 1 job ) / ( T hrs )
--------------------------------------------
I can say:
+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+
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The time, +T+ has to be less than +6+ hrs
no matter how slow Joseph is.
--------------------
Suppose Joseph is the slowest and takes
+12+ hrs to do the job alone
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+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+
+1%2F8+%2B+1%2F6+%2B+1%2F12+=+1%2FT+
Multiply both sides by +24T+
+3T+%2B+4T+%2B+2T+=+24+
+9T+=+24+
+T+=+2.667+ hrs
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If Joseph happens to be faster than the other two,
the job will get done in LESS than Joseph's time
Example:
Joseph's rate is +1%2F2+
+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+
+1%2F8+%2B+1%2F6+%2B+1%2F2+=+1%2FT+
+3T+%2B+4T+%2B+12T+=+24+
+19T+=+24+
+T+=+1.2632+ hrs