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machines x, y, and z - HELP!

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gmatpup: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Sat Oct 15, 2011 6:38 pmFollowed by: 1 member; Thanked: 1 times

by gmatpup » Sat Nov 19, 2011 4:27 pm

I encountered this question on the test... but I am not sure how to answer it.. I do not have the answer choices unfortunately so if anyone can help that would be awesome!

The question went something like this:

Machine X, Y, and Z were able to fill a lot in 3, 5, and 9 hours respectively. If they were to work together simultaneously, how long would it take them to fill 2/3 of the lot?

Thanks so much!

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Source: Beat The GMAT — Problem Solving | Sat Nov 19, 2011 4:27 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sat Nov 19, 2011 4:47 pm

Machine X can fill 1/3 rd of the lot in 1 hour
Machine Y can fill 1/5 th of the lot in 1 hour
Machine Z can fill 1/9 th of the lot in 1 hour.
Machines X,Y,Z can fill (1/3)+(1/5)+(1/9) = 29/45 th of the lot in 1 hour

Working simultaneously,
29/45 of the the lot can be filled in 1 hour
then 30/45=(2/3) of the lot can be filled in ??

?? = 30/29 hours

Hope it helps !

Anil Gandham
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Nov 19, 2011 5:15 pm

gmatpup wrote:I encountered this question on the test... but I am not sure how to answer it.. I do not have the answer choices unfortunately so if anyone can help that would be awesome!

The question went something like this:

Machine X, Y, and Z were able to fill a lot in 3, 5, and 9 hours respectively. If they were to work together simultaneously, how long would it take them to fill 2/3 of the lot?

Thanks so much!

Let the job = LCM of 3, 5 and 9 = 45 units.
Rate for X = w/t = 45/3 = 15 units per hour.
Rate for Y = w/t = 45/5 = 9 units per hour.
Rate for Z = w/t = 45/9 = 5 units per hour.
Combined rate for X+Y+Z = 15+9+5 = 29 units per hour.
2/3 of the job = (2/3)*45 = 30 units.
Time for X+Y+Z = w/r = 30/29 hours.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Nov 20, 2011 12:38 am

gmatpup wrote:I encountered this question on the test... but I am not sure how to answer it.. I do not have the answer choices unfortunately so if anyone can help that would be awesome!

The question went something like this:

Machine X, Y, and Z were able to fill a lot in 3, 5, and 9 hours respectively. If they were to work together simultaneously, how long would it take them to fill 2/3 of the lot?

Thanks so much!

let the total work be 45 units ( LCM of 3,5 & 9 )

Efficiency of machines -

X = 45/3 =>15 units/hr

Y = 45/5 => 9 units/hr

Z = 45/9 = > 5 units/hr

So they will produce 29 units/hr( 15 + 9 + 5 ) ....

They want to produce 2/3 of 45 units => 30 units...

Thus time taken by all of them is 30 /29 hrs => 1.xx hrs

Abhishek

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