Aileen and emily are college roommates. working together it takes them 45 minutes to clean their room. today is aileen's day to clean. she can clean the room by herself in 2/3 the time emily takes by herself. how long, in minutes, will it take aileen to clean the room by herself?

The solution for this problem is:

Let time taken by Emily be x

then Aileen take 2/3 of x = 2x/3

1 min work of Emily = 1/x

1 min work of Aileen = 1 / 2x/3 = > 3/2x

1 min work of both = 1/45

1/x + 3/2x = 1/45

5/2x = 1/45

1/x = 2/225

Emily take 225/2 mins to complete the work, then Aileen

= 225/2*2/3

= 75 mins.