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# help

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Rosa and leann are working on a group English assignment. They each write one essay alone and then one essay together. Leann takes 6 hours longer than rosa to write her individual essay. Writing at the same rate, they complete their combined essay in 4 hours. How long does it take leann to write her individual essay?

Feb 10, 2020

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Let  the number of hours that  Rosa takes to write her essay  =  x

So....each hour.....she completes   1/x   of the essay

And the number  of hours  that Leann takes to write her essay  =  x + 6

So....each hour.....she completes  1 / [ x + 6]   of the essay

So....working together  they take  4  hours to complete the essay.....which means that each hour working together, they complete (1/4)  of the essay

So  we have that

1/x  +  1 / [ x + 6]  =  1/4

[x + 6 + x ]            1

__________  =   ___

x (x + 6)               4

2x + 6               1

________  =   ____              cross-multiply

x^2 + 6x            4

4 ( 2x + 6)  =  x^2 + 6x

8x + 24  = x^2  + 6x     rearrange as

x^2  - 2x  - 24   =   0      factor

(x - 6) ( x + 4)  =  0

Setting the first factor to 0  and solving  for  x    gives that  x  = 6

So...it takes Leann   x + 6 =   6 + 6   = 12  hrs to write the essay by herself   Feb 10, 2020