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dferm: Master | Next Rank: 500 Posts; Posts: 446; Joined: Thu Jul 26, 2007 1:07 pm; Thanked: 6 times

by dferm » Mon Mar 24, 2008 12:38 pm

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

A. 3
B. 4
C. 6
D. 9
E. 12

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Source: Beat The GMAT — Problem Solving | Mon Mar 24, 2008 12:38 pm

xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

by xilef » Mon Mar 24, 2008 12:58 pm

using work formula to find the time it takes for both machines to do the same work:

(18*36)/54=12 hrs for both machines to complete the job

2 hrs is 6 times faster so the company needs 6 of each to do it in 12hr.

Answer C.

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preciousrain7: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Dec 06, 2007 4:16 pm; Location: NYC, NY; Thanked: 2 times

by preciousrain7 » Mon Mar 24, 2008 1:47 pm

xilef wrote:using work formula to find the time it takes for both machines to do the same work:

(18*36)/54=12 hrs for both machines to complete the job

2 hrs is 6 times faster so the company needs 6 of each to do it in 12hr.

Answer C.

Can you give more explanation for the last step please? Thanks!

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xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

by xilef » Mon Mar 24, 2008 2:04 pm

It takes both working together (one of each machine) to do the job in 12hrs. The company used the same number of each type of machine to do the job in 2 hours, which is 6 times faster than the the time it takes one of each machine to do the job, therefore, company used 6 of each.

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preciousrain7: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Dec 06, 2007 4:16 pm; Location: NYC, NY; Thanked: 2 times

by preciousrain7 » Mon Mar 24, 2008 2:31 pm

xilef wrote:It takes both working together (one of each machine) to do the job in 12hrs. The company used the same number of each type of machine to do the job in 2 hours, which is 6 times faster than the the time it takes one of each machine to do the job, therefore, company used 6 of each.

thanks!

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daduck112: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Jul 31, 2007 5:08 am

by daduck112 » Mon Jul 07, 2008 12:09 pm

another way to look at things...

R does 1/36 the job

S does 1/18 the job

R+S = 1/12 the job or 12 hours to do 1 job

you want to do it in 2 hours....

so you you'll 12/2 = {6 machines each.}

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Mon Jul 07, 2008 3:05 pm

1/36 + 1/18 = 1/12 so together they can do 1 job in 12 hours. Then, I set up the following equation:

2/1/12 = x/1/2 [translation: if 2 machines complete 1 job in 12, then how many machines will complete 1 job in 2 hours?]

24 = 2x

x = 12 machines, 6 of each type.

https://second-lap.blocked/

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Tue Sep 08, 2009 10:56 am

This is an interesting problem which can be solved in another way(rather a cryptic way). Thought of sharing this.
let the n be the number of machines.
We know the rates of the machines as 1/36 and 1/18.
Both working together for 2 hrs will do
2/36 + 2/18 amount of work.
Now we know n machines finished the work in 2 hrs.
So the equation will be
n*(2/36 + 2/18) = 1 (=1 coz the work got completed).
(This is the famous Logitech approach)

solving n = 6

HT Helps

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