You add them together and subtract 1 because the total amount stays the same throughout the entire problem and you have to find the amount of water in the glass that is not full when the other glass is full. 10/12 + 8/15 = 50/60 + 32/60 = 82/60. 82/60 - 60/60 = 22/60, which simplifies to 11/30.
