Two pipes A and B can empty a full tank in 20 hours and 25 hours respectively. In how many hours will tank be emptied when they are opened together?

Answer

To solve the problem of how long it will take for pipes A and B to empty a full tank when opened together, we can follow these steps:

### Step 1: Determine the time taken by each pipe to empty the tank
- Pipe A can empty the tank in 20 hours.
- Pipe B can empty the tank in 25 hours.

### Step 2: Find the total work done in terms of the least common multiple (LCM)
- The LCM of 20 and 25 is 100. This means we can consider the total work (the full tank) as 100 units.

### Step 3: Calculate the efficiency of each pipe
- Efficiency of Pipe A = Total work / Time taken by A = 100 / 20 = 5 units/hour.
- Efficiency of Pipe B = Total work / Time taken by B = 100 / 25 = 4 units/hour.

### Step 4: Calculate the combined efficiency of both pipes
- Combined efficiency of A and B = Efficiency of A + Efficiency of B = 5 + 4 = 9 units/hour.

### Step 5: Calculate the total time taken to empty the tank when both pipes are opened together
- Total time = Total work / Combined efficiency = 100 / 9 hours.

### Step 6: Convert the time into hours and minutes if necessary
- 100 / 9 hours is approximately 11.11 hours, which can be converted into hours and minutes:
- 11 hours and (0.11 * 60) minutes = 11 hours and 6.67 minutes, which is approximately 11 hours and 7 minutes.

### Final Answer
The tank will be emptied in approximately **11 hours and 7 minutes** when pipes A and B are opened together.

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