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

Question

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. 30
B. 45
C. 60
D. 90
E. 120

Show Answer

Official Answer

D

A. 30
B. 45
C. 60
D. 90
E. 120

motki · Answer

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

Bunuel · Answer

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

damiani256 · Answer

How do I know when to use W= 1 vs assign a variable for work?

Krunaal · Answer

Here's some theory for Work word problems: https://gmatclub.com/forum/work-word-pr ... 87357.html There's no rule that you should consider work as 1 or keep it as W in any particular type of problem, it depends on what you find easier to work with - at times you can also take W as LCM of the Rates, or Times given in the question.

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

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

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