It takes one machine 25 minutes to pick a bale of cotton and another machine 30 minutes to compete the same job. if both machines are used, how long will it take them to pick a bale of cotton?

The first machine works at the rate x = 1 bale/ 25 min.
The second machine works at the rate y = 1 bale/30 min.

The combined rate is
x + y = 1/25 + 1/30 bales/min
         = (30 + 25)/(25*30) = 55/750
         = 11/150 bales/min

The time for both machines to pick 1 bale of cotton is
(1 bale)/(11/150 bales/min) = 150/11 min = 13.64 min

13.6 minutes

No solution : there is no number of boxes that she bought