A pipe can empty a tank in 12 minutesand another pipe can empty it in 16 minutes.If both thepipes are opned simultaneously,find the time in which a full tank is emptied----

Options

A. 6 minutes
B. 6 1/7 minutes
C. 6 2/7 minutes
D. None of these

Answer

To solve the problem of how long it takes for two pipes to empty a tank when opened simultaneously, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the time taken by each pipe to empty the tank:**
- Pipe A can empty the tank in 12 minutes.
- Pipe B can empty the tank in 16 minutes.

2. **Calculate the rate of work for each pipe:**
- The rate of Pipe A = 1 tank / 12 minutes = 1/12 tanks per minute.
- The rate of Pipe B = 1 tank / 16 minutes = 1/16 tanks per minute.

3. **Find the combined rate of both pipes when opened together:**
- Combined rate = Rate of Pipe A + Rate of Pipe B
- Combined rate = (1/12 + 1/16) tanks per minute.

4. **Calculate the least common multiple (LCM) of the denominators (12 and 16) to add the fractions:**
- The LCM of 12 and 16 is 48.
- Convert the rates to have a common denominator:
- (1/12) = 4/48
- (1/16) = 3/48
- Combined rate = (4/48 + 3/48) = 7/48 tanks per minute.

5. **Determine the time taken to empty the full tank:**
- If both pipes together can empty 7/48 of the tank in one minute, then the time taken to empty 1 full tank is the reciprocal of the combined rate:
- Time = 1 / (7/48) = 48/7 minutes.

6. **Convert the time into minutes and seconds (if necessary):**
- 48/7 minutes = 6.857 minutes, which is approximately 6 minutes and 51 seconds.

### Final Answer:
The time taken to empty the full tank when both pipes are opened simultaneously is approximately **6 minutes and 51 seconds**.