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# Someone please solve following question using "ratio" and "proportion" strategy.?

John ad Mary operate automatic splitters for fireplace wood. John's machine can split a pile of wood in 4 days. Mary machine can do the same job in 3 days. They work 8 hours per day. How long it will take them to split the pile of wood using both machines?

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- openzgateLv 41 decade agoFavorite Answer
John can do 1/4 of the job in one day.

Mary can do 1/3 of the job in one day.

In one day, if they work together they can complete 7/12 of the job. This is because 1/4+1/3=7/12. So this is their rate or how fast they can work.

Now, (rate) times (time) = how much of the job they can do. So, we know that 7/12 • x = 1 (complete job). x is the number of days. Solve for x such that it completes the complete job.

So x = 12/7 = 1 5/7

(1/4 + 1/3)(1 5/7) = 1

So it will take 1 5/7 days

Have fun.

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