SOLUTION: Mike can repaint a dog house three times faster than miguel. If they work together, it will take them 4 days to complete the job. How long would it take for mike to do the repainti

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Mike can repaint a dog house three times faster than miguel. If they work together, it will take them 4 days to complete the job. How long would it take for mike to do the repainti      Log On


   

Question 1044061: Mike can repaint a dog house three times faster than miguel. If they work together, it will take them 4 days to complete the job. How long would it take for mike to do the repainting alone?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Put all the information into the form of a table. 
PERSON             RATE as JOB/DAYS

MIKE                 3%2Fx

MIGUEL               1%2Fx

BOTH TOGETHER        1%2F4


The "BOTH" rate is the sum of their individual rates.

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The choice made for the variable, x, was for the time for Miguel to to ONE whole repaint job by himself. According to given description, Mike's rate would be three times that of Miguel, so 3%2A%281%2Fx%29=3%2Fx.

Solve the equation, 3%2Fx%2B1%2Fx=1%2F4.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Mike can repaint a dog house three times faster than miguel. If they work together, it will take them 4 days to complete the job. How long would it take for mike to do the repainting alone? 
Let time Mike takes be M

Then time Miguel takes is 3M

We then get the following equation: 1%2FM+%2B+1%2F%283M%29+=+1%2F4

Solve this for M, or time Mike takes. You should get: highlight_green%28matrix%281%2C4%2C+16%2F3%2C+or%2C+5%261%2F3%2C+days%29%29