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An inlet pipe fills a tank in 20 minutes, while an outlet pipe empties it in 60 minutes. Starting with an empty tank, how long will it take to fill half of the tank if both are opened?
15 minutes
20 minutes
30 minutes
10 minutes
15 minutes
Use the product/difference formula: T=BтИТAA├ЧBтАЛ for filling the full tank, then divide by 2 for half the tank.
Inlet pipe fills a tank in 20 minutes; outlet pipe empties the same tank in 60 minutes.
Time=Net┬аEfficiencyTotal┬аWorkтАЛ
Use the product/difference formula: T=BтИТAA├ЧBтАЛ for filling the full tank, then divide by 2 for half the tank.
Students often calculate the time for the full tank (30 minutes) and forget the question specifically asks for half of the tank.
Calculate LCM as Total Capacity
Assume the total capacity of the tank is the LCM of 20 and 60, which is 60 units.
Total┬аCapacity=60┬аunits
Determine Pipe Efficiencies
Efficiency of the inlet pipe is 60/20=3 units/min. Efficiency of the outlet pipe is 60/60=1 unit/min.
Net┬аEfficiency=3тИТ1=2┬аunits/min
Calculate Time for Half Tank
Half of the tank capacity is 60/2=30 units. Time required is 30/Net┬аEfficiency.
Time=230тАЛ=15┬аminutes
A is correct because the net filling rate is 2 units/minute, and it takes 15 minutes to fill the required 30 units of capacity.
This logic is identical to Relative Speed problems in Time-Speed-Distance where two objects move in opposite directions; here, filling is positive and emptying is negative velocity.