Question 738575
let sasha take x hours to clean the house. which is 1 job

so she does 1/x of the job in 1 hour

Miranda takes x+12 hours to do the job
so 1/(x+12) of the job is done in 1 hour

 {{{1/x +1/(x+12)}}} of the job they do in 1 hour

{{{ ((x+12)+x)/(x(x+12)) }}} 

{{{(2x+12)/(x(x+12))}}}

to complete the job they will take {{{(x(x+12))/(2x+12)}}}hours

{{{(x(x+12))/(2x+12)}}} = {{{8}}}

Solve

{{{x^2+12x=8(2x+12)}}}


{{{x^2+12x=16x+96}}}


rearrange

{{{x^2-4x-96=0}}}

{{{x^2-12x+8x-96=0}}}


{{{x(x-12)+8(x-12)=0}}}

(x-12)(x+8)=0

x=12 OR x=-8

Ignore negative

x= 12 hours --------- sasha's time to complete the job alone