SOLUTION: It takes John 3 times as long as it takes Jessica to mow a lawn. If it took them both 11 hours to mow the lawn, how long would it take John to mow the lawn alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes John 3 times as long as it takes Jessica to mow a lawn. If it took them both 11 hours to mow the lawn, how long would it take John to mow the lawn alone?       Log On


   

Question 964689: It takes John 3 times as long as it takes Jessica to mow a lawn. If it took them both 11 hours to mow the lawn, how long would it take John to mow the lawn alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It takes John 3 times as long as it takes Jessica to mow a lawn. If it took them both 11 hours to mow the lawn, how long would it take John to mow the lawn alone?
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John's rate:: 1/(3x) job/hr
Jessica's rate: 1/x job/hr
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Together rate:: 1/11 job/hr
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Equation::
rate + rate = together rate
1/(3x) + 1/x = 1/11
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11x + 33x = x*3x
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3x^2 - 44x = 0
x(3x-44) = 0
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Non-zero solution::
x = 44/3
Ans: John's time to do the job alone = 3x = 3(44/3) = 44 hours
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Cheers,
Stan H.
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