A tank when full can be emptied by an outlet pipe A in 5.6 hours, while an inlet pipe B can fill the same empty tank in 7 hours. If pipes A and B are turned on alternatively for 1 hour each starting with pipe A when the tank is full, how long will it take to empty the tank?
47 hours
Given:
- Outlet Pipe A can empty the full tank in 5.6 hours.
- Inlet Pipe B can fill the empty tank in 7 hours.
- Pipes operate alternately for 1 hour each, starting with Pipe A.
Step 1: Work Done by Each Pipe in 1 Hour
- Pipe A empties: 1/5.6 of the tank per hour.
- Pipe B fills: 1/7 of the tank per hour.
Step 2: Net Work Done in 2 Hours (One Cycle)
One cycle consists of:
- 1st Hour (Pipe A): 1/5.6 of the tank is emptied.
- 2nd Hour (Pipe B): 1/7 of the tank is filled.
Net emptying in 2 hours:
1/5.6 - 1/7 = 10/56 - 8/56 = 2/56 = 1/28 of the tank.
Step 3: Total Time Required
Since 1/28 of the tank is emptied in 2 hours, the full tank will be emptied in:
28 × 2 = 56 hours.
However, in the last cycle, after 46 hours, only 1/28 of the tank remains.
Pipe A alone can empty this in 1 more hour.
Final Answer: 47 hours
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