TIaO - Part 2

Number Theory Level 2

Jeremy has a tank with three inlets. He knows that the first inlet can fill the tank in $20$ hours. He also knows that the second one can fill the tank in $24$ hours. He does not know how many hours will it take for the third inlet to fill the tank. He opens the three inlets simultaneously, and discovers that the three can fill it in $8$ hours. How many hours can the third inlet fill the tank by itself?

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

30

hours

25

hours

40

hours

15

hours

1 solution

Nelson Mandela
Jan 2, 2015

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

so the time taken by the third inlet (in hours) to fill up the tank is T.

total time = 8 hours

$\frac { 1 }{ 8 } =\frac { 1 }{ 20 } +\frac { 1 }{ 24 } +\frac { 1 }{ T }$ .

impiles, $\frac { 1 }{ T } =\frac { 1 }{ 8 } -\frac { 1 }{ 24 } -\frac { 1 }{ 20 }$

LCM = 120.

thus, T = 120/(15-5-6) = 120/4 = $\boxed{30}$ hours.

TIaO - Part 2

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