Question asks "If machine A produces K liters of fluid in 10 minutes and machine B produces K liters in 15 minutes, what is the time it takes to produce a liter?" I understand the correct answer would be to add $K/15 + K/10$
However, if I instead choose to add minutes/liter together, what does is the interpretation of this? I'm not quite sure what is the physical meaning of $15/K + 10/K = 25/K$
It seems like it's saying "if it takes a machine 10 minutes to produce K liters and another machine 15 minutes to produce K liters, then the total time it takes is 25 minutes to produce K liters", so I just flip this ratio it becomes K liters per 25 minutes which is wrong. I don't understand what happened.
Let a = K/15, and b = K/10. The correct answer would be 1/(a + b). However, when you take the reciprocals of a and b, add them together, and then take the reciprocal of that, you get 1/(1/a+1/b). This can be simplified to yield ab/(a+b). Hence, to me, this answer doesn't have any significance (other than having the same units as the correct answer).