A cistern can be filled by a tap in 6 hours and emptied by an outlet pipe in 7.5 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?
30 hours
To solve this problem, we need to determine the time it takes to fill the cistern when both the tap and the outlet pipe are open simultaneously. First, we calculate the rate at which each operates:
- The tap can fill the cistern in 6 hours, thus it fills of the cistern per hour.
- The outlet pipe empties the cistern in 7.5 hours, meaning it empties per hour.
To find their combined rate, subtract the outlet pipe's rate from the tap's rate:
This combined rate means the cistern is filled at a rate of per hour when both are open. Therefore, the cistern will be completely filled in:
30 hours
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