For a certain bathtub, it takes the hot water faucet 4 times as long to fill the tub as it does the cold water faucet. Left on together, the two faucets take 4 minutes to fill the tub. How long will it take the hot water faucet to fill the tub by itself? Do not do any rounding.

Step 1 ：Let's denote the time it takes for the cold water faucet to fill the tub by itself as \(x\). Then, the time it takes for the hot water faucet to fill the tub by itself is \(4x\).

Step 2 ：When both faucets are on, they fill the tub in 4 minutes. This means that in one minute, they fill \(\frac{1}{4}\) of the tub.

Step 3 ：The cold water faucet fills \(\frac{1}{x}\) of the tub in one minute, and the hot water faucet fills \(\frac{1}{4x}\) of the tub in one minute.

Step 4 ：So, we can set up the equation \(\frac{1}{x} + \frac{1}{4x} = \frac{1}{4}\) to solve for \(x\).

Step 5 ：The solution to the equation is \(x = 5\). This means that the cold water faucet takes 5 minutes to fill the tub by itself.

Step 6 ：Therefore, the hot water faucet, which takes 4 times as long, will take \(4*5 = 20\) minutes to fill the tub by itself.

Step 7 ：Final Answer: The hot water faucet will take \(\boxed{20}\) minutes to fill the tub by itself.