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Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both are opened together, how long will it take to fill the tank?
5 hours
6 hours
8 hours
12 hours
6 hours
Use the product divided by sum rule: (10├Ч15)/(10+15)=150/25=6. This takes less than 10 seconds to calculate.
Pipe A fills the tank in 10 hours. Pipe B fills the tank in 15 hours.
T=a+ba├ЧbтАЛ
Use the product divided by sum rule: (10├Ч15)/(10+15)=150/25=6. This takes less than 10 seconds to calculate.
Many students incorrectly calculate the average time by doing (10+15)/2=12.5, failing to account for the efficiency of the combined work rates.
Define individual work rates
Pipe A fills 1/10 of the tank per hour, and Pipe B fills 1/15 of the tank per hour.
RateAтАЛ=101тАЛ,RateBтАЛ=151тАЛ
Calculate combined work rate
Add the rates of both pipes together to find the total work done in one hour.
101тАЛ+151тАЛ=303+2тАЛ=305тАЛ=61тАЛ
Find the total time
The time taken to fill the tank is the reciprocal of the combined hourly rate.
T=1/61тАЛ=6┬аhours
B is correct because the combined work rate of 1/6 tank per hour results in a total time of 6 hours.
This inverse proportion logic is identical to solving 'Time and Work' problems where two people complete a task together; always remember that Time=1/Work┬аRate.