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

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:
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