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Question 1121818: Ezra can type a research paper in 8 hours.
Micah helped Ezra in typing,and together they finished in 6 hours.
How long will take Micah to finish the job if she worked alone??
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ezra can type a paper in 8 hours.
when micha helped ezra, they finished the paper in 6 hours.
ezra's rate is 1/8 of the paper in one hour.
their combined rate is 1/6 of the paper in one hour.
when they work together their rates are additive.
therefore 1/8 + x = 1/6, where x represents micha's rate.
subtract 1/8 from both sides of this equation to get:
x = 1/6 - 1/8 = 4/24 - 3/24 = 1/24
that should be miika's rate of work.
to test if this is true, use the combined rate formula.
(r1 + r2) * time = quantity of work produced
this would become (1/8 + 1/24) * 6 = 1
(1/8 + 1/24) is the combined rate.
6 is the number of hours to complete 1 paper.
1 is the quantity of work produced which is 1 paper.
divide both sides of this formula by 6 to get (1/8 + 1/24) = 1/6
1/8 is equivalent to 3/24.
3/24 + 1/24 is equal to 4/24 which is equal to 1/6.
at the rate of 1/24 of the paper in 1 hour, micha would take 24 hours to complete the same paper when working alone.
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