SOLUTION: A farmer working with his son needs 3 hours to plow a field. The farmer working alone can plow the field in 12 hours. How long would it take the son working alone to plow the field

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A farmer working with his son needs 3 hours to plow a field. The farmer working alone can plow the field in 12 hours. How long would it take the son working alone to plow the field      Log On


   

Question 228212: A farmer working with his son needs 3 hours to plow a field. The farmer working alone can plow the field in 12 hours. How long would it take the son working alone to plow the field?
Please provide a detailed explanation of the steps taken in a problem like this. Thank You
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer working with his son needs 3 hours to plow a field. The farmer working alone can plow the field in 12 hours. How long would it take the son working alone to plow the field?
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Together DATA:
time = 3 hrs/job ; rate = 1/3 job/hr
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Farmer DATA:
time = 12 hrs/job ; rate = 1/12 job/hr
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Son's DATA:
time = x hrs/job ; rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/12 + 1/x = 1/3
Multiply thru by 12x to get:
x + 12 = 4x
3x = 12
x = 4 hrs (time the son requires to do the job alone)
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Cheers,
Stan H.