Hi,

I have this problem I'm trying to figure out:

Jamal can fill the vending machine in 45 minutes. When his sister, Violet, helps him, it takes them 20 minutes. How long would it take Violet to fill the machine by herself?

The solution formula the textbook provides is:

20/x + 20/45 = 1

This is confusing to me, because shouldn't the logic of it work like this:

Work by Jamal/Total Work by both + Work by Violet (x)/ Work by both = 1

, or 45/20 + x/20 = 1?

P.S. I know that often they recommend to break down work rate to a unit of time. So, in Jamal's case it would be 1/45, and total rate would be 1/20. So, in that case 1/45:1/20, actually, would mean 20/45. But is 1/45:1/20 + x:1/20 = 1? Isn't 1 a 100%, and in this case 1 is what?? I'm confused

Thank you for any help whatsoever.