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Pipe A can fill a tank in 12 hours, and Pipe B can fill it in 18 hours. If both are opened together, how long will it take to fill the tank?
7.2 ┬аhours
7.5 ┬аhours
8.0 ┬аhours
8.4 ┬аhours
7.2 ┬аhours
Use the product-over-sum formula T=12+1812├Ч18тАЛ to save time in the exam hall.
Pipe A can fill the tank in 12 hours, and Pipe B can fill it in 18 hours.
T=x+yxyтАЛ
Use the product-over-sum formula T=12+1812├Ч18тАЛ to save time in the exam hall.
Adding the rates directly as 1/12+1/18 and forgetting to take the reciprocal at the final step, or incorrectly adding the time values (12+18=30).
Find Total Work (LCM)
Assume the total capacity of the tank is the LCM of 12 and 18, which is 36 units.
LCM(12,18)=36
Calculate Individual Rates
Pipe A's 1-hour work is 36/12=3 units/hour, and Pipe B's 1-hour work is 36/18=2 units/hour.
RAтАЛ=3,RBтАЛ=2
Calculate Combined Rate
When both pipes are opened together, their combined 1-hour work is 3+2=5 units/hour.
RcombinedтАЛ=3+2=5
Calculate Total Time
Divide the total capacity by the combined rate to find the total time required: 36/5=7.2 hours.
T=536тАЛ=7.2┬аhours
A is correct because working together, the pipes take exactly 7.2 hours to fill the tank.
This inverse-proportional relationship between rates and time is identical to speed, distance, and time problems involving relative motion.
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