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Pipe A can fill a tank in 12 hours and Pipe B can empty it in 20 hours. If both are opened simultaneously, how long will it take to fill the tank?
30 hours
25 hours
35 hours
40 hours
30 hours
Assume total capacity is the LCM of 12 and 20 (60 units). Pipe A's rate is +5 units/hr, Pipe B's rate is -3 units/hr, giving a net rate of 2 units/hr.
Pipe A fills a tank in 12 hours and Pipe B empties it in 20 hours.
T=yтИТxx├ЧyтАЛ
Assume total capacity is the LCM of 12 and 20 (60 units). Pipe A's rate is +5 units/hr, Pipe B's rate is -3 units/hr, giving a net rate of 2 units/hr.
Adding the rates of both pipes instead of subtracting the emptying pipe's rate from the filling pipe's rate.
Find Total Capacity using LCM
Take the LCM of the individual times (12 and 20) to assume a total tank capacity of 60 units.
LCM(12,20)=60┬аunits
Calculate Individual Rates
Pipe A's filling rate is 1260тАЛ=+5 units/hr, and Pipe B's emptying rate is 2060тАЛ=тИТ3 units/hr.
RAтАЛ=+5,RBтАЛ=тИТ3
Determine Net Rate
When both pipes are open simultaneously, the net filling rate is the difference between the two rates: 5тИТ3=2 units/hr.
RnetтАЛ=5тИТ3=2┬аunits/hr
Calculate Total Time
Divide the total capacity by the net rate to find the time taken to fill the tank: 260тАЛ=30 hours.
T=260тАЛ=30┬аhours
A is correct because the net filling rate of both pipes is 301тАЛ of the tank per hour, resulting in a total time of 30 hours to fill the tank.
This inverse rate approach is identical to relative speed problems in Time, Speed, and Distance where two objects move in opposite directions.
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