Question 1100984
<br>
First the standard method of solution, usually taught in beginning algebra classes....<br>
The two tubs together fill the tub in 4 minutes; so they fill 1/4 of the tub in 1 minute.<br>
The cold water faucet fills the tub alone in 12 minutes; so it fills 1/12 of the tub in 1 minute.<br>
So the fraction of the tub that the hot water faucet fills in 1 minute is {{{1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6}}}<br>
Since the hot water faucet can fill  1/6 of the tub in 1 minute, it can fill the tub in 6 minutes.<br>
Algebraically, if x is the number of minutes is takes the hot water faucet to fill the tub alone,
{{{1/12 + 1/x = 1/4}}}
{{{1/x = 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6}}}
{{{x = 6}}}<br><br>
And here is an alternative solution method which I find many students prefer....<br>
The cold water faucet can fill the tub in 12 minutes.
In those same 12 minutes, the two faucets together could fill the tub 3 times.
But if together they can fill the tub 3 times in 12 minutes, and the cold water faucet alone can fill it only 1 time in 12 minutes, then the hot water faucet can fill the tub 2 times in 12 minutes.
But that means it can fill the tub once in 6 minutes.<br>
Try both methods for solving this kind of problem and find which "workd' better for you.