Question

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

Answer 1

\[\frac{11\times 12}{11+12}\] is the short quick answer

Answer 2

we can work through all the steps, but in the end that is what you will get

Answer 3

how

Answer 4

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

Answer 5

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

Answer 6

Thank You

Answer 7

yw