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
Middle tap alone 1 12
Large tap alone 1 5
All three together 1 x
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The equation comes from
+ + =
+ + =
Clear of fractions by multiplying through by the LCD of 60x, and
solve the equation.
Answer: x = 3 minutes.
Edwin