Problem: An inlet pipe can fill an oil tank in three days, while a smaller inlet pipe can fill the same tank in six days. If both pipes are used, how long will it take to fill the tank?an

Direction: Read and analyze the problem carefully, provide illustration if possible and translate the problem into mathematical equation, then solve for the number of days.

Task: Provide a complete solution to the problem.

Solution:answer 

Let's assume that the volume of the oil tank is 1 unit.

### Problem Analysis:

We are given two pipes with different flow rates:

1. **Larger inlet pipe**: Fills the tank in 3 days.
2. **Smaller inlet pipe**: Fills the tank in 6 days.

We need to determine how long it will take to fill the tank if both pipes are used simultaneously.

### Step 1: Determine the rate of each pipe.

- The larger inlet pipe fills the tank in 3 days, so its rate is \(\frac{1}{3}\) of the tank per day.
- The smaller inlet pipe fills the tank in 6 days, so its rate is \(\frac{1}{6}\) of the tank per day.

### Step 2: Combine the rates.

When both pipes are used together, their combined rate is the sum of their individual rates:

\[
\text{Combined Rate} = \frac{1}{3} + \frac{1}{6}
\]

### Step 3: Simplify the combined rate.

To add the fractions, find a common denominator:

\[
\frac{1}{3} = \frac{2}{6}
\]

So,

\[
\text{Combined Rate} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
\]

### Step 4: Determine the time required to fill the tank.

The combined rate \(\frac{1}{2}\) means that together, the two pipes fill \(\frac{1}{2}\) of the tank in 1 day. To fill the entire tank:

\[
\text{Time} = \frac{1}{\text{Combined Rate}} = \frac{1}{\frac{1}{2}} = 2 \text{ days}
\]

### Final Answer:

It will take **2 days** to fill the tank if both pipes are used simultaneously.

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Would you like more details or have any questions? Here are 5 related questions to consider:

1. How would the time change if the smaller pipe could fill the tank in 4 days instead of 6 days?
2. What if the larger pipe were twice as fast as the smaller one? How would that affect the filling time?
3. How much of the tank would be filled after 1 day if both pipes were used?
4. What is the effect on the filling time if the smaller pipe is closed halfway through?
5. How would the solution change if a third pipe, filling the tank in 12 days, is also opened?

**Tip:** When solving problems involving rates, it’s often helpful to think of the task as a “work problem,” where each component contributes a fraction of the task per unit of time.

Learn how to calculate the time required to fill a tank using two inlet pipes of different capacities. This problem involves rates and work problems, exploring how to combine rates to determine filling time. Suitable for students in Grades 7-9.

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