Let's denote the time it would take the larger pump to fill the tank alone as \( T \) hours. 

The small pump fills the tank in 4 hours, so its rate is \( \frac{1}{4} \) of the tank per hour. 

The larger pump fills the tank in \( T \) hours, so its rate is \( \frac{1}{T} \) of the tank per hour.

When both pumps work together, their combined rate is the sum of their individual rates, which is \( \frac{1}{4} + \frac{1}{T} \) of the tank per hour.

We are given that when working together, they fill the tank in \( 0.4444444444444444 \) hours, which can be simplified as \( \frac{4}{9} \) hours (since \( 0.4444444444444444 \) is a repeating decimal that is equivalent to \( \frac{4}{9} \)).

So, the combined rate of the two pumps working together is \( \frac{1}{\frac{4}{9}} \) of the tank per hour, which simplifies to \( \frac{9}{4} \) of the tank per hour.

Now we can set up the equation:

\[ \frac{1}{4} + \frac{1}{T} = \frac{9}{4} \]

To solve for \( T \), we first find a common denominator for the fractions on the left side of the equation, which is \( 4T \):

\[ \frac{T}{4T} + \frac{4}{4T} = \frac{9}{4} \]

Simplifying the left side, we get:

\[ \frac{T + 4}{4T} = \frac{9}{4} \]

Now we can cross-multiply to solve for \( T \):

\[ 4(T + 4) = 9(4T) \]

\[ 4T + 16 = 36T \]

Subtract \( 4T \) from both sides:

\[ 16 = 32T \]

Divide both sides by 32:

\[ T = \frac{16}{32} \]

\[ T = \frac{1}{2} \]

So, it would take the larger pump \( \frac{1}{2} \) hour, or 30 minutes, to fill the tank alone.
더 큰 펌프가 탱크를 채우는 데 걸리는 시간을 \( T \) 시간으로 표시해 보겠습니다.

작은 펌프는 4시간에 탱크를 채우므로 그 속도는 시간당 탱크의 \( \frac{1}{4} \).

더 큰 펌프는 \( T \시간 동안 탱크를 채우므로 그 속도는 시간당 탱크의 \( \frac{1}{T} \).

두 펌프가 함께 작동할 때, 두 펌프의 합산 속도는 개별 속도의 합으로, 시간당 탱크의 \( \frac{1}{4} + \frac{1}{T} \).

두 펌프가 함께 작동할 때 0.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444