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Pipe A is 3 times faster than pipe B. Both pipes together fill a tank in 36 min. How much time will pipe A alone take to fill the tank?
156 min
80 min
48 min
100 min
48 min
Since Pipe A is 3 times faster than Pipe B, the ratio of time taken is 1:3. Total work rate is 3+1=4 parts of B's work. Pipe A takes 36├Ч4=144 minutes for total work divided by its efficiency factor, or simply 36├Ч(1+31тАЛ)=48 minutes.
Pipe A is 3 times faster than pipe B. Together they fill the tank in 36 minutes.
TAтАЛ=RAтАЛ1тАЛ,TBтАЛ=RBтАЛ1тАЛ,TAтАЛ1тАЛ+TBтАЛ1тАЛ=TtotalтАЛ1тАЛ
Since Pipe A is 3 times faster than Pipe B, the ratio of time taken is 1:3. Total work rate is 3+1=4 parts of B's work. Pipe A takes 36├Ч4=144 minutes for total work divided by its efficiency factor, or simply 36├Ч(1+31тАЛ)=48 minutes.
Many students mistake the '3 times faster' to mean time is 3 times, whereas time is actually inversely proportional to speed (1/3 the time).
Define Efficiency Ratio
Let the work rate (efficiency) of pipe B be x. Since pipe A is 3 times faster, its rate is 3x.
RAтАЛ=3x,RBтАЛ=x
Calculate Combined Work Rate
When working together, their combined rate is 3x+x=4x. Given they fill the tank in 36 minutes, total capacity is rate ├Ч time.
Capacity=4x├Ч36=144x
Calculate Time for Pipe A
To find the time taken by A alone, divide the total capacity by Pipe A's rate.
TAтАЛ=3x144xтАЛ=48┬аmin
C is correct because Pipe A fills the tank in 48 minutes based on the inverse ratio of their speeds.
This concept of inverse proportionality between speed and time is fundamental in Pipe & Cistern, Time & Distance, and Work & Wages problems.
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