SOLUTION: the larger of two pipes can fill a tank twice as fast as the smaller pipes. together the two pipes require 20 minutes to fill the tank. find the number of minutes required for the

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Question 537398: the larger of two pipes can fill a tank twice as fast as the smaller pipes. together the two pipes require 20 minutes to fill the tank. find the number of minutes required for the larger pipe to fill.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
the larger of two pipes can fill a tank twice as fast as the smaller pipes. together the two pipes require 20 minutes to fill the tank. find the number of minutes required for the larger pipe to fill.
               Tanks      Time in      Rate in       
              filled      minutes    tanks/minute
Larger pipe                  

Smaller pipe

Both together

Fill in x for the time for the larger, And since the smaller
pipe takes twice as long, fill in 2x for the smaller pipe's
time.  Fil in the 20 minutes it takes both pipes together
to fill 1 tank:

               Tanks      Time in      Rate in       
              filled      minutes    tanks/minute
Larger pipe                  x                 

Smaller pipe                2x

Both together               20

In all three cases exactly 1 tank is being filled, so
we put 1 for the tanks filled in every case

               Tanks      Time in      Rate in       
              filled      minutes    tanks/minute
Larger pipe      1           x                 

Smaller pipe     1          2x

Both together    1          20

next fill in the rates in tanks/min by putting tanks over
minutes:

               Tanks      Time in      Rate in       
              filled      minutes    tanks/minute
Larger pipe      1           x          1%2Fx                   
Smaller pipe     1          2x          1%2F%282x%29 
Both together    1          20          1%2F20

The equation comes from:

               %28matrix%283%2C1%2CLarger%2C%22pipe%27s%22%2Crate%29%29 + %28matrix%283%2C1%2CSmaller%2C%22pipe%27s%22%2Crate%29%29 = %28matrix%284%2C1%2Crate%2Cof%2Cboth%2Ctogether%29%29  
                        1%2Fx + 1%2F%282x%29 = 1%2F20   

Clear of fractions and solve for x.

Answer:  x = 30 minutes

Edwin