Question

A and B working together complete a price of work in 6 days , while A alone can do it in 9 days. How much time will B alone take to finish it?​

Answer 1

Step-by-step explanation:

A and B working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time would B take to finish it alone?

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You can do this a few ways. I use the formula:

(AxB)/(A+B)=6 or (9xB)/(9+B)=6

now you can plug both sides of the equation into a graphing calculator and where they intersect will be the amount of days for B to finish.

The other option is to plug a value value in for B and reduce until it = 6. Whichever number (B) makes the equation work is the answer in days for B to do the job alone.

(9x18)/(9+18)=6

(162/27)=6

6=6

therefore the amount of days it takes B to do it alone is 18 days.

hope this helps. This formula only works when dealing with 2 “people” doing the work. When dealing with more than 2 workers, you will have to say 1/9 of the work is done by A in 1 day and 1/B of the work is done by B in one day and 1/C work is done by C in one day and basically have to use a graphic calculator. You can solve without it but it’s a pain to do so. This is something you’ll see on an SAT so graphing calculators are the way to go.

hope this helps

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• ( A + B ) can do a work in 6 days
• A alone can do the work in 9 days

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• B alone can do the work in = ???

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{1\: day \: Work = \dfrac{1}{Total\: time\: taken \: to\: complete\: the \: work}}}}}$

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$\sf :\implies{\bold{ (A+B)'s\: one\: day\: work = \dfrac{1}{6} }}$

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$\sf :\implies{\bold{ A 's\: one\: day\: work = \dfrac{1}{9} }}$

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Now ; let B's one day work be x

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$\sf :\implies{\bold{ \dfrac{1}{6} = \dfrac{1}{9} + x} }$

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$\sf :\implies{\bold{ x = \dfrac{1}{6} - \dfrac{1}{9} }}$

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$\sf :\implies{\bold{ x = \dfrac{3 + 2 }{18}} }$

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$\sf :\implies{\bold{ x = \dfrac{5}{18} }}$

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B's one day work = 5 / 18

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$\sf{\red{\boxed{\bold{1\: day \: Work = \dfrac{1}{Total\: time\: taken \: to\: complete\: the \: work}}}}}$

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$\sf :\implies{\bold{ \dfrac{5}{18} = \dfrac{1}{Total\: time \: taken } } }$

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$\sf :\implies{\bold{ Total\: time\:taken = \dfrac{1}{\dfrac{5}{18}} }}$

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$\sf :\implies{\bold{ Total\: time\: taken = 1 \div \dfrac{5}{18} }}$

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$\sf :\implies{\bold{ Total\: time\: taken = 1 \times \dfrac{18}{5} } }$

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$\sf :\implies{\bold{ Total\: time\: taken = 3.6 days }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• B alone will take 3.6 days to complete the work