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?
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