SOLUTION: A water tank can be filled by any combination of 3 different taps . With the smallest tap the tank can be filled in 20 mins. With the middle tap the tank can be filled in 12 mins.

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Question 569785: A water tank can be filled by any combination of 3 different taps . With the smallest tap the tank can be filled in 20 mins. With the middle tap the tank can be filled in 12 mins. With the largest tap the tank can be filled in 5 minutes .How long does it take to fill the tank with all 3 taps running ?
Explain your reasoning.
Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
A water tank can be filled by any combination of 3 different taps . With the smallest tap the tank can be filled in 20 mins. With the middle tap the tank can be filled in 12 mins. With the largest tap the tank can be filled in 5 minutes .How long does it take to fill the tank with all 3 taps running?
Make this chart:

                     number of         minutes         rate in     
                   tanks filled       required       tanks/minute
Small tap alone

Middle tap alone

Large tap alone

All three together

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Let the answer be x minutes, so fill in x for the number of minutes
required for all three.  Also fill in 20, 12, and 5 for the minutes
required for the others 

                     number of         minutes         rate in     
                   tanks filled       required       tanks/minute
Small tap alone                          20

Middle tap alone                         12

Large tap alone                           5

All three together                        x

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In each of the 4 cases, exactly 1 tank is filled, so we put 1 for the
number of tanks filled in each of the 4 cases

                     number of         minutes         rate in     
                   tanks filled       required       tanks/minute
Small tap alone         1                20

Middle tap alone        1                12

Large tap alone         1                 5

All three together      1                 x

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Then we fill in the rates in tanks/minute by dividing the number
of tanks filled by the number of minutes required:

                     number of         minutes         rate in     
                   tanks filled       required       tanks/minute
Small tap alone         1                20           1%2F20 
Middle tap alone        1                12           1%2F12 
Large tap alone         1                 5            1%2F5 
All three together      1                 x            1%2Fx

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        The equation comes from

         %28matrix%285%2C1%2C%0D%0A%0D%0Arate%2Cfor%2Csmall%2Ctap%2Calone%29%29 + %28matrix%285%2C1%2C%0D%0A%0D%0Arate%2Cfor%2Cmiddle%2Ctap%2Calone%29%29 + %28matrix%285%2C1%2C%0D%0A%0D%0Arate%2Cfor%2Clarge%2Ctap%2Calone%29%29 = %28matrix%285%2C1%2C%0D%0A%0D%0Arate%2Cfor%2Call%2Cthree%2Ctogether%29%29  

             1%2F20 + 1%2F12 + 1%2F5 = 1%2Fx          

Clear of fractions by multiplying through by the LCD of 60x, and
solve the equation.

Answer: x = 3 minutes.

Edwin