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Pipe A can fill a tank in 12 hours and Pipe B can empty it in 18 hours. If both are opened together, how many hours will it take to fill the tank?
36
30
24
40
36
Assume total capacity = LCM(12, 18) = 36 units. Net efficiency per hour = 3тИТ2=1 unit, giving time = 36/1=36 hours.
Pipe A fill time = 12 hours, Pipe B empty time = 18 hours
Time=tBтАЛтИТtAтАЛtAтАЛ├ЧtBтАЛтАЛ
Assume total capacity = LCM(12, 18) = 36 units. Net efficiency per hour = 3тИТ2=1 unit, giving time = 36/1=36 hours.
Adding the rates of both pipes (121тАЛ+181тАЛ) instead of subtracting the emptying pipe's rate.
Assume Total Capacity
Take the LCM of individual operational times (12 and 18) as the total capacity in units.
LCM(12,18)=36┬аunits
Determine Individual Rates
Calculate work done per hour for filling pipe A and emptying pipe B.
EAтАЛ=1236тАЛ=+3┬аunits/hr,EBтАЛ=1836тАЛ=тИТ2┬аunits/hr
Calculate Combined Net Rate
Subtract the emptying rate of pipe B from the filling rate of pipe A.
Net┬аEfficiency=3тИТ2=1┬аunit/hr
Calculate Total Time
Divide total capacity by the combined net efficiency.
Time=136тАЛ=36┬аhours
A is correct because working together the net fill time is 36 hours.
This opposing-rate framework is structurally identical to relative speed calculations for objects moving in opposite directions or downstream-upstream analysis.
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