Jane works twice as fast as her daughter anna. if it takes 15 minutes to clean the kitchen together, how long would it take anna to clean the kitchen by herself?

Here, Twice fast means, she takes half time in doing same amount of work.
Let, Anna takes = 2t & Jane takes = t

It would be: 1/t + 1/2t = 1/15
2t + t / 2t² = 1/15
15(3t) = 2t²
2t² = 45t
Divide both sides by t, 
2t = 45
t = 45/2
t = 22.5
& 2t = 22.5(2) = 45

In short, Anna would take 45  minutes

Hope this helps!