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

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23 Jan 2011, 01:54

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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?

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

Please Explain....

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.

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