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rates and production of fiber

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rates and production of fiber

by LevelOne » Sat Jun 20, 2009 10:36 pm
Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 5 hours. How many hours will it take machines A, B, and C, operating together at their respective rates, to produce 1,000 feet of the fiber?

I solved it as below, however the official explanation was quite different than my calculations. Can you make a few suggestions, how you would solve it, pls? Thanks!

rates:
1/2 -> machine A
1/3 -> machine B
1/5 -> machine C

1/2 + 1/3 + 1/5 = 5/6 + 1/5 = 25/30 + 6/30 = 31/30

30/31*2 = 60/31
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by rah_pandey » Sun Jun 21, 2009 3:37 am
The approach should be
in 1 hour how much each machine can produce
500/2,500/3,500/5

therefore working together in one hour they will produce
500/2+500/3+500/5
=500(15+10+6)/30
=(500*31)/30

thus for making 1000 feet time reqd
=1000*30/(500*31)
=60/31

your soln is effective and has no problems if you are sure what you were doing. Explaining it and may understanding it becomes difficult.
2 in your soln can be written as 1000/500

where 500*31/30= amt produced in 1 hour
therefore 1000 feet would be produced in
=(1000*30)/(500*31)=(1000/500)*(30/31)=2*30/31
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by LevelOne » Sun Jun 21, 2009 5:32 am
rah_pandey, thanks for the comparison your solution is the same as in
the official source. i might go by this method for the future problems.
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Re: rates and production of fiber

by Ian Stewart » Sun Jun 21, 2009 11:55 am
LevelOne wrote:Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 5 hours. How many hours will it take machines A, B, and C, operating together at their respective rates, to produce 1,000 feet of the fiber?
An alternative to using the formula: Let's call producing 500 feet 'one job'. The question asks how long it takes A, B and C take to do two jobs - that will take twice as long as doing one job. Converting each machine to the same amount of time:

A does 15 jobs in 30 hours
B does 10 jobs in 30 hours
C does 6 jobs in 30 hours
A+B+C do 31 jobs in 30 hours
A+B+C do 1 job in 30/31 hours

So they do 2 jobs in 60/31 hours.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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