Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

So far this is what I got:

Rate Distance Time

Cathies 3x 1 1/3x

Beth 2x 1 1/2x

Abbie x 1 1/x

I then did (1/2x)+(1/3x)+(1/x)=1

Can someone explain to me where I keep going wrong? Thanks