Two pipes empty a vat in 1hr and 12 min. When one pipe is used to fill and one to empty the vat, it is filled in 3 hrs. How long would it take each pipe to empty the vat if only one pipe is open?
x - time of emptying the vat with the first pipe
y - operating time of the second pipe
First pipe alone - (1vat/x minute)(x minute) = 1vat
Second pipe alone - (1vat/y minute)(y minute) = 1vat
Total time 72minute, then 72/x + 72/y = 1 (1)
1/x - amount emptied by the outlet pipe in one hour
1/y - amount filled by the inlot pipe in one hour
1/180 - amount filled by both pipe in one hour (3 hours × 60 = 180 minute)
Then 1/x - 1/y = 1/180 (2)
divide by 72 equation (1)
Substitute x in the first equation
Answer: First pipe - 1 hour 43 minute. Second pipe - 3 hours 59 minute. During this time, each pipe alone will do the work
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