>>14380692>It's double the harmonic mean of these times. Algebraic solution, I'm asking for an intelligent answer, not the old formalism of applying formulas
>That's because the harmonic mean is how long it'd take for two copies of A, B, and C to do it,Is "harmonic mean" a subject in arithmetic? You could at least care to explain why the "harmonic mean" gives how long it would take for 2 groups of facuets A, B, and C to fill a tank.
I think I know what the explanation is because it is the official (algebraic) solution, which uses a lot more intuition to explain.
It is based on the idea that if a faucet fills a tank in 10 hours for example, in 1 hour it fills 1/10 of the same tank.
In this question, in 1 hour you would fill 1/7 of the tank using faucets A and B, which has to be equal to 1/A + 1/B
In 1 hour you would fill 1/8 of the same tank using faucets A and C, which has to be equal to 1/A + 1/C
In 1 hour you would fill 1/9 of the same tank using faucets B and C, which has to be equal to 1/B + 1/C
From those can form the equation
2/A + 2/B + 2/C = 1/7 + 1/8 + 1/9
This equation has an actual meaning too, it means in 2 hours, faucet A, B and C fill 1/7 + 1/8 + 1/9 of the tank. From there you just need to use ratios and proportions.
>and doubling that gives you how long A B and C would take.This is and fine and good if you're solving it algebraically as you're describing what happens to the variables.
>>14380884it is "simpler" in the way applying a one line formula is simpler than writing what you thoughts in 10 lines.
You're mistaking simplicity with cohesiveness, which don't get me wrong it's not incorrect in other contexts, but not in this one. I'm also not calling you dumb or anything, you were just trained for formalism, which if works for you then no harm done.
Let me give you an example of another very easy question so you understand what I mean by simplicity of solution. (will post in another post as reply to this one)
