Question

Tom can clean the living room in 45 minutes. Wally can clean it in 30 minutes. 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?

Answer 1

Let the job of cleaning the room be 1 unit

Tom's rate = 1/45
Wally's rate = 1/30
combined rate = 1/45 + 1/30 = 1/18 room/min
job left to be done after 5 minutes
= 1 - 5(1/18) = 13/18

let Gigi's rate be 1/x
so total combined rate = 1/18 + 1/x
= (x+18)/(18x)

so (13/18) ÷ (x+18)/(18x) = 7
(13/18)(18x)/(x+18) = 7
13x = 7x + 126

x = 21

It would take Gigi 21 minutes to do the room herself.