Question 674178
Tom can clean the living room in 45 minutes.
 Wally can clean it in 30 minutes. 
If both start cleaning and 5 minutes later, their sister Gigi joins them, taking
 them 7 minutes more to finish.
 How long would it take Gigi to clean the living room alone?
:
let g = Gigi's time to do the job alone (in minutes)
let the completed job = 1 (a spotless living room)
:
A shared work equation. (T and W worked a total of 5+7 = 12 minutes)
{{{12/45}}} + {{{12/30}}} + {{{7/g}}} = 1
Multiply by 90g to clear the denominators, cancel and you have:
2g(12) + 3g(12) + 90(7) = 90g
24g + 36g + 630 = 90g
630 = 90g - 60g
630 = 30g
g = 630/30
g = 21 minutes, GG working alone
:
:
;
See if that checks out using a calc
12/45 + 12/30 + 7/21 = 
.267 + .400 + .333 = 1, confirms our solution of 21 minutes