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One pipe can fill a tank in 20 min, while another pipe can empty it in 30 min. If both pipes are opened together on an empty tank, how long (in min) will it take to fill half of the tank?
20
30
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30
Given: Pipe A fills tank in 20 min, Pipe B empties tank in 30 min.
Pipe A fills tank in 20 min, Pipe B empties tank in 30 min.
T=Net┬аRateWorkтАЛ
Use the formula T=yтИТxxyтАЛ for the full tank, then divide the result by 2 to find the time for half the tank.
Students often forget to calculate the time for 'half' the tank and provide the answer for the 'full' tank.
Find the net efficiency
Let the total capacity be the LCM of 20 and 30, which is 60 units. Efficiency of pipe A = 60/20=3 units/min. Efficiency of pipe B (emptying) = тИТ60/30=тИТ2 units/min.
Net┬аRate=3тИТ2=1┬аunit/min
Calculate time for full tank
To fill the total 60 units, the time taken is calculated by dividing total capacity by net rate.
TfullтАЛ=160тАЛ=60┬аmin
Calculate time for half tank
Since the question asks for the time to fill half the tank, we take half of the total time.
ThalfтАЛ=260тАЛ=30┬аmin
B is correct because the net rate is 1 unit/min, taking 60 minutes for a full tank, thus 30 minutes for half the tank.
This concept of 'Net Rate' is identical to 'Relative Speed' in Time, Speed, and Distance problems where two objects move in opposite directions.