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If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

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\[\frac{6\times 4}{6+4}\] is a start
how did you get the formula satellite?
if you do two of these you will see it

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one has a rate of \(\frac{1}{6}\) the other a rate of \(\frac{1}{4}\) the combined rate is the sum \(\frac{1}{6}+\frac{1}{4}=\frac{4+6}{6\times 4}\) you want to solve rate times time equals one job, i.e. \[\frac{4+6}{6\times 4}t=1\] so \[t=\frac{6\times 4}{4+6}\]
you can work it out step by step for each problem and get the same answer, but if you have to do more than one of these, say adam eats an apple if m minutes, eve eats an apple in n minutes, together they can eat the apple in \[\frac{m\times n}{m+n}\] minutes saves time , especially on a test or quiz

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