Pipe A alone takes only 40% of the time taken by pipe B alone to fill an empty tank. When an outlet pipe C is also opened simultaneously with pipe A and pipe B, it takes 3/4 more time to fill the empty tank than it takes, when only pipe A and pipe B are opened together. If it takes 15 hours to fill when all the three pipes are opened simultaneously, then in how much time (in hours) can pipe C empty the full tank operating alone? 
01) 12 
02)18 
03) 20
04) 24

Let the time taken by pipe B to fill the tank alone be \( t_B \) hours. From the problem, we know that pipe A takes 40% of the time taken by pipe B, meaning pipe A takes \( 0.4t_B \) hours to fill the tank.

### Step 1: Determine the rates of the pipes
- The rate of pipe B (filling rate) is \( \frac{1}{t_B} \) tanks per hour.
- The rate of pipe A is \( \frac{1}{0.4t_B} = \frac{2.5}{t_B} \) tanks per hour.

When both pipes A and B are open together, their combined rate of filling the tank is:
\[
\text{Rate of A and B together} = \frac{2.5}{t_B} + \frac{1}{t_B} = \frac{3.5}{t_B} \text{ tanks per hour}.
\]

### Step 2: Filling time with pipes A, B, and C together
When pipe C is also opened, the time to fill the tank increases by \( \frac{3}{4} \) more time compared to only A and B. Let the rate at which pipe C empties the tank be \( \frac{1}{t_C} \) tanks per hour.

So, the combined rate of pipes A, B, and C is:
\[
\text{Rate of A, B, and C} = \frac{3.5}{t_B} - \frac{1}{t_C}.
\]

Given that it takes 15 hours to fill the tank with all three pipes open, the rate at which the tank is filled when all three pipes are open is \( \frac{1}{15} \) tanks per hour. Therefore, we have the equation:
\[
\frac{3.5}{t_B} - \frac{1}{t_C} = \frac{1}{15}.
\]

### Step 3: Filling time with only pipes A and B
The time taken to fill the tank with only pipes A and B is less, and the problem says that the time taken with pipe C open is \( \frac{7}{4} \) times the time taken with only A and B. Therefore, the time to fill the tank with only pipes A and B is:
\[
\frac{7}{4} \times 15 = 60 \div 7 = 8.57 \text{ hours}.
\]

Thus, the rate at which pipes A and B together fill the tank is:
\[
\frac{1}{8.57}.
]
This  forms thedifference of5minutes idealst

Pipe A alone takes only 40% of the time taken by pipe B alone to fill an empty tank. When an outlet pipe C is also opened simultaneously with pipe A and pipe B, it takes 3/4 more time to fill the empty tank than it takes when only pipe A and pipe B are opened together. If it takes 15 hours to fill when all three pipes are opened simultaneously, then in how much time (in hours) can pipe C empty the full tank operating alone? 01) 12 02)18 03) 20 04) 24

Solve a pipe work problem where Pipe A takes 40% of the time of Pipe B to fill a tank, and Pipe C empties the tank. Learn how to calculate the time taken by Pipe C to empty the full tank using work rate formulas. Suitable for students in Grades 9-11.

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