Video: Rational Equations Word Problem: Eliminating Solutions, under Pre-Calculus/Rational Functions Playlist

Problem: Two hoses are used to fill a pond in 12 minutes. One hose can fill the pond ten minutes faster than the other hose, if used alone. How long does each hose take to fill the pond by itself?

Why is it incorrect to set up an equation using the slow hose as a variable, like this:

(1/s) + (1/(s-10)) = 1/12

Versus setting it up the way Sal did it, with using the fast hose as the variable:

(1/f) + (1/(f+10)) = 1/12

I understand, mechanically, that you don't get the correct answer using the slow hose in the mental model, I just don't understand why it is incorrect to think about the equation that way.