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Question
One tap can fill a cistern in 3 hours and the waste pipe can empty the full cistern in 5 hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?
Solution
One tap can fill a cistern in = 3 hours
A waste pipe can empty a cistern in = 5 hours
∴ One tap 1-hour work =`1/3`
Waste pipe 1-hour work =`1/5`
∴ One tap and waste pipe together 1-hour work
`=1/3-1/5=(5-3)/15`
`=2/15`
∴ The empty cistern will be full in =`15/2` hours
`=7 1/2` hours
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