Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?

One Answer on this Question

1. X filling rate is 1/18 or 4/72 per hour

   Y filling rate is 1/24 or 3/72 per hour

   Combined as a pair it’s 7/72 in a complete 2 hour alternating sequence

   72+ 7/72 =10 sequences = 70/72 on 20 hours, The outstanding balance is just 2/72

   So at 20.5 hours with X turn filling is 100% complete with 72/72

   Answer: It will take 20.5 hours to completely fill this tank.

   Analysis of measured filling process, from X = 42/72 share & from Y = 30/72 share

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