GMAT Prep Work Rates Question

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CMP.1: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Wed Sep 14, 2011 11:23 am

by CMP.1 » Tue Apr 24, 2012 12:01 pm

Could I kindly ask whether someone could explain the method to solving this particular type of rates question for me please?

I am looking to take the GMAT (3rd Attempt) one last time before the new IR section is introduced on June the 5th.....last shot, praying I get it right this time!

Question: Six machines, each working at the same constant rate, can complete a job in 12 Days. How many additional machines, each working at the same constant rate, would be required to complete the task in 8 Days?

Many thanks for all your help,

Chris

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Source: Beat The GMAT — Problem Solving | Tue Apr 24, 2012 12:01 pm

gschaefer: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Feb 08, 2011 3:52 am; Thanked: 1 times

by gschaefer » Tue Apr 24, 2012 12:43 pm

here is one way to get to the solution:

you know that 6 machine can complete the job in 12 days.
This means that 1 machine can do the job in 72 Days since all machines work at the same constant rate.
In order to find the number of machine which are needed to do the job in 8 days you have to divide 72 days by 8 days and get 9 machine

9-6 = 3 so 3 new machines are required to complete the job.

I hope this explanation helps you

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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 » Tue Apr 24, 2012 12:45 pm

6 machines can complete a job in 12 days. So,
1 machine can complete the same job in 12*6 days
x machines can complete the same job in 12*6/x days

Total number of days = 12*6/x = 8 days(From the question stem)
So 12*6/8 = x
x = 9.
9 machines can complete the same job in 12*6/9(=8)days. So, we need 3 additional machines to complete the task in 8 Days.

But the best way is to remember that Machine(Person) days = Constant (For same units of work).
i.e. # of persons or machines * # of days = Constant.(For same units of work)
Case 1: # of persons or machines * # of days = 6 * 12
Case 2: # of persons or machines * # of days = x * 8
Since, # of persons or machines * # of days = Constant, 6 * 12 = x * 8. So the value of x = 9

and yes, don't worry about your exam. I am sure you are going to crack the 680 mark this time round. Good luck with your preparation.

Anil Gandham
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CMP.1: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Wed Sep 14, 2011 11:23 am

by CMP.1 » Tue Apr 24, 2012 1:12 pm

Thank you both very much for such prompt and well explained replies, I am most grateful! The silly thing is I actually managed to get to the "9" part, but couldnt work out where to go from there, or see the logic as to where the answer lay from that point in.

Thankfully thats another question issue ive managed to crack thanks to your help so fingers crossed for the rest.

Chris

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed Apr 25, 2012 2:40 am

You have to use the Man Days formula that we learn in the time and work chapter.

It says that M1 X D1 = M2 X D2

If 12 men were required to do a job in 10 days, how many days will 15 men take...

Apply the above formula here and you get the answer as 9 overall and 3 additional machines.

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Hope my post would have helped you Dude...

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Wed Apr 25, 2012 9:56 am

Dear CMP,
Please note that speeds can be arithmetically added to each other, so you can exploit the concept to solve the problems on work and speed.

Here, Rate of six machines working together = 1/12 day^-1. therefore speed of each machine = 1/(6*12) day^-1
Now required speed = 1/8 day^-1. Hence number of machines required = (1/8) / (1/72) = 9
So extra machines = 9-6 = 3

Follow your passion, Success as perceived by others shall follow you

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