If a pipe can fill a tank in 2h and another pipe can fill the same take in 6h,then what part of a tank will be filled by both the pipes in 1 h, if they are opened simultaneously?

Answer

To solve the problem, we need to determine how much of the tank will be filled by both pipes when they are opened simultaneously for 1 hour.

### Step-by-Step Solution:

1. **Determine the filling rates of each pipe:**
- Pipe A can fill the tank in 2 hours. Therefore, in 1 hour, Pipe A fills:
\[ \text{Rate of Pipe A} = \frac{1 \text{ tank}}{2 \text{ hours}} = \frac{1}{2} \text{ tank per hour} \]

- Pipe B can fill the tank in 6 hours. Therefore, in 1 hour, Pipe B fills:
\[ \text{Rate of Pipe B} = \frac{1 \text{ tank}}{6 \text{ hours}} = \frac{1}{6} \text{ tank per hour} \]

2. **Add the filling rates of both pipes:**
- When both pipes are opened simultaneously, the total rate of filling the tank is:
\[ \text{Total Rate} = \text{Rate of Pipe A} + \text{Rate of Pipe B} = \frac{1}{2} + \frac{1}{6} \]

3. **Find a common denominator to add the fractions:**
- The least common multiple (LCM) of 2 and 6 is 6. Therefore, we convert \(\frac{1}{2}\) to have a denominator of 6:
\[ \frac{1}{2} = \frac{3}{6} \]
- Now we can add the fractions:
\[ \text{Total Rate} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \text{ tank per hour} \]

4. **Determine the part of the tank filled in 1 hour:**
- Since both pipes together fill \(\frac{2}{3}\) of the tank in 1 hour, the part of the tank filled by both pipes in 1 hour is:
\[ \text{Part filled in 1 hour} = \frac{2}{3} \]

### Final Answer:
The part of the tank that will be filled by both pipes in 1 hour, when opened simultaneously, is \(\frac{2}{3}\).

---