TIaO - Part 3

Number Theory Level 2

A tank has two inlets and an outlet (a pipe that removes water from the tank). The first inlet can fill a tank in 36 36 hours, while the second one can fill it in 27 27 hours. The outlet can empty the tank in 18 18 hours. How many hours will it take to fill up the tank?

Note:

  • The inlets and outlets are positioned so that the tank can be filled evenly.

This problem is part of the set Tank Inlets and Outlets - Work Problems .

96 96 hours 120 120 hours The tank will never be full. 108 108 hours

Jeremy Bansil by Jeremy Bansil , 27, Philippines

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2 solutions

Curtis Clement
Jan 2, 2015

Let x {x} = time to fill take , so by taking the inputs and outputs into account x {x} [ 1/2 + 2/3 -1] = x 6 \frac{x}{6} = 18. ∴ \therefore x {x} = 108

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Nelson Mandela
Jan 2, 2015

As the problem is of a tank filling, the relationship is inverse.

so the total time (in hours to fill up the tank) is T.

1 T = 1 36 + 1 27 − 1 18 \frac { 1 }{ T } =\frac { 1 }{ 36 } +\frac { 1 }{ 27 } -\frac { 1 }{ 18 } .

LCM = 108.

so, T = 108 3 + 4 − 6 \frac { 108 }{ 3+4-6 } = 108 \boxed{108} hours.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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