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# A constructor is using three water filling pumps, X,Y, and Z

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Intern
Joined: 27 Sep 2010
Posts: 27

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A constructor is using three water filling pumps, X,Y, and Z [#permalink]

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23 Jan 2011, 02:54
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A constructor is using three water filling pumps, X,Y, and Z, working together at their respective constant rates to fill an initially empty tank in 9 hours.Pumps X and Y,working together at their respective constant rates can fill the same tank in 10 hours.How many hours will pump Z, working alone at its constant rate, take to fill the same tank?

[Reveal] Spoiler:
90

(i don't have the answer choices for the question above.)

Last edited by MichelleSavina on 23 Jan 2011, 06:49, edited 1 time in total.

Kudos [?]: 84 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 41701

Kudos [?]: 124836 [2], given: 12079

Re: Three water filling pumps, X,Y, and Z, working together [#permalink]

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23 Jan 2011, 04:03
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MichelleSavina wrote:
Q) A constructor is using three water filling pumps, X,Y, and Z, working together at their respective constant rates to fill an initially empty tank in 9 hours. Pumps X and Y,working together at their respective constant rates can fill the same tank in 10 hours. How many hours will pump Z, working alone at its constant rate, take to fill the same tank?

A) 90

Let the times needed for the pumps X, Y, and Z, working ALONE at their respective constant rates to fill the empty tank be x, y and z respectively.

Given: $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{9}$$ (remember we can add the rates) and $$\frac{1}{x}+\frac{1}{y}=\frac{1}{10}$$.

Subtract 2 from 1: $$\frac{1}{z}=\frac{1}{9}-\frac{1}{10}=\frac{1}{90}$$ --> $$z=90$$.

Or: you can notice that as all 3 pumps can fill the empty tank in 9 hours and only X and Y can fill the tank in 10 hours, so they need 1 more hour, then Z is doing in 9 hours the work done by X and Y in this 1 extra hour, so as X and Y need total of 10 hours to fill the empty tank then Z alone will need 9*10=90 hours to fill the empty tank alone.

Several important things you should know to solve work problems with examples:
word-translations-rates-work-104208.html#p812628
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Kudos [?]: 124836 [2], given: 12079

Intern
Joined: 05 Nov 2010
Posts: 1

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Re: Three water filling pumps, X,Y, and Z, working together [#permalink]

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23 Jan 2011, 03:55
Let A be total work,

Given 1). A/(X+Y+Z)=9
Given 2). A/(X+Y)=10

Question is A/Z = ?

From given 1) and 2), we know that 9(X+Y+Z)=10(X+Y), therefore 9Z=(X+Y)=A/10

A/Z = 90

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Re: A constructor is using three water filling pumps, X,Y, and Z [#permalink]

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14 Feb 2017, 00:31
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Re: A constructor is using three water filling pumps, X,Y, and Z   [#permalink] 14 Feb 2017, 00:31
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