Problem Solving

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

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

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.

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

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.

Show spirit and move ahead. Do not get disheartened. Everybody is sailing in the same ship of GMAT on this site named BTG...

Don't give up Come what may and you will see yourself scoring a 700+...

Hope my post would have helped you Dude...

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