how long does it take leann to finish her essay

Question

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?

Answer 1

1/R + 1/L = 1/4 substitute R=L-6

1/(L-6) + 1/L = 1/4

multiply by 4L(L-6) to eliminate the fractions

4L + 4L-24 = L^2 -6L

L^2 -14L + 24 = 0

factor

(L-12)(L-2) = 0

L=12 hours alone for Lena ignore L=2 as it makes Rosa's time negative

R= 12-6 = 6 hours alone for Rosa

1/6 + 1/12 = 3/12 = 1/4