TIaO - Part 1

Number Theory Level 1

An inlet (a pipe that lets water enter a tank) can fill a tank in $12$ hours. Another inlet can fill the same tank in $15$ hours. A third inlet can fill the tank in $10$ hours. If the three inlets are opened simultaneously, in how many hours will the tank be full?

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

4

hours

5

hours

3

hours

2

hours

1 solution

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.

$\frac { 1 }{ T } =\frac { 1 }{ 12 } +\frac { 1 }{ 15 } +\frac { 1 }{ 10 }$ .

LCM = 60.

so, T = 60/(5+4+6) = 60/15 = $\boxed{4}$ hours.

TIaO - Part 1

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