anonymous
  • anonymous
Brandon can paint a fence in 12 hours and Elaine can paint fence in 11 hours.How long will they take to paint the fence if they work together
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{11\times 12}{11+12}\] is the short quick answer
anonymous
  • anonymous
we can work through all the steps, but in the end that is what you will get
anonymous
  • anonymous
how

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anonymous
  • anonymous
brandon's rate is \(\frac{1}{12}\) of the fence per hour elaine's rate is \(\frac{1}{11}\) of the fence per hour their combined rate is the sum of these two, namely \[\frac{11+12}{11\times 12}\] you want to see how long it takes to complete one job, so set \[\frac{11+12}{11\times 12}t=1\] and solve for \(t\) in one step: \[t=\frac{11\times 12}{11+12}\] as promised
anonymous
  • anonymous
at the first step when you add \[\frac{1}{12}+\frac{1}{11}\] you can go ahead and write \[\frac{1}{12}+\frac{1}{11}=\frac{23}{132}\] then when you solve \[\frac{23}{132}t=1\] you get \[t=\frac{132}{23}\] but if you do more than one of these, or if you have a test, you can do it quickly as i wrote above
anonymous
  • anonymous
Thank You
anonymous
  • anonymous
yw

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