SOLUTION: It takes josh 2/3 as long as it takes beth to paint a wall. if together josh and beth would take 12 hours, how long would it take beth to do the work alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes josh 2/3 as long as it takes beth to paint a wall. if together josh and beth would take 12 hours, how long would it take beth to do the work alone?      Log On


   

Question 388900: It takes josh 2/3 as long as it takes beth to paint a wall. if together josh and beth would take 12 hours, how long would it take beth to do the work alone?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
It takes josh 2/3 as long as it takes beth to paint a wall. if together josh and beth would take 12 hours, how long would it take beth to do the work alone?
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Let Beth time be "x"; her rate is 1/x job/hr
Then Josh time is (2x)/3 ; his rate is 3/(2x) job/hr
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Together time = 12 hrs; their rate = 1/12 job/hr
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Equation:
rate + rate = together rate
1/x + 3/(2x) = 1/12
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Multiply thru by 12x:
12 + 18 = x
x = 30 hrs: Beth's time to do the job.
(2/3)x = 20 hrs; Josh's time to do the job.
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Cheers,
Stan H.