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A tap fills a tank in 11 hours. Another tap empties the full tank in 22 hours. How long (in hours) will it take to fill the tank completely, if the tank is empty and both the taps are open together? 3937
23
22
25
24
22
Use the formula DifferenceProductтАЛ when one tap fills and another empties: 22тИТ1111├Ч22тАЛ=1111├Ч22тАЛ=22 hours.
Tap A fills the tank in 11 hours, Tap B empties the tank in 22 hours.
T=yтИТxxyтАЛ
Use the formula DifferenceProductтАЛ when one tap fills and another empties: 22тИТ1111├Ч22тАЛ=1111├Ч22тАЛ=22 hours.
Students often add the rates (111тАЛ+221тАЛ) thinking both are filling, forgetting that the outlet tap subtracts from the total efficiency.
Calculate individual efficiencies
Assuming total capacity is the LCM of 11 and 22, which is 22 units. Tap A efficiency = 22/11=+2 units/hr. Tap B efficiency = 22/22=тИТ1 unit/hr.
EffnetтАЛ=2тИТ1=1┬аunit/hr
Calculate total time
To find the time taken when both taps are open, divide the total capacity by the net efficiency.
Time=EffnetтАЛTotal┬аCapacityтАЛ=122тАЛ=22┬аhours
B is correct because the net work done per hour is 1 unit, so it takes 22 hours to fill 22 units of capacity.
This concept of net efficiency is identical to problems involving relative speed where two objects move in opposite directions on a track.