knight247 wrote:Hey Thouraya,
There are multiple approaches to this problem. I'm sure you know the formula Rate=Work/Time.
If you want to factor in the people involved there is a similar formula you can use. Rate=Work/(People*Time). This kinda makes it a lot easier.

Now in our problem let the work to be done be the printing of 96 pages. Now, here people=machines... Now, whether we have 6 machines or more, the rate that each one works at is the same.

For the 6 machines, we have Rate=96/(6*12) and for the larger number of machines we have 96/(x*8) where x is the number of machines and 8 is the given time as per the problem. Now, both these rates are equal. So 96/(6*12)=96/(x*8)

Solving we get x=9. So 9 machines will finish the job in 8 hrs. 9-6=3 Hence B. All clear?? If you need to know other methods then let me know.

Liarish wrote: Hey knight247,

Thanks a lot for this formula "Rate=Work/(People*Time)", it has worked perfectly for a number of work questions that I have done. But I was wondering if we could use the same formula for the problem below. Could you please show me how ?

Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?
1:600
2:800
3:1000
4:1200
5:1500

Answer is : A

Thanks a ton!

GMATGuruNY wrote:

Thouraya wrote:Hi Mitch,

I like your second approach if it always works. I have a question on your first approach, please:

If I want to assume that every machine produces two units (instead of 1), then 6 machines produce 12 units a day, and 12 x 12= 144 units in 12 days.

If I want to produce the 144 units in 8 days instead, then 144/8 ?

Also, I cant cross multiple in work problems cuz I have three variables: days, machines, and units?

Thank you!

The second approach that I used is just a variation of the rate formula: rate * time = work.

In the problem above, rate = number of machines, so (number of machines) * (number of days) = work.

Since the work must remain the same no matter how many machines are used, we get the following inverse proportion:

(number of machines) * (number of days) = (number of machines) * (number of days)

If the number of machines goes up, the number of days must go down, so that the amount of work stays the same. If the number of machines goes down, the number of days must go up, so that the amount of work stays the same. This is the definition of an inverse proportion. As one value goes up, the other goes down, so that the product never changes.

1*30 = 30
2*15 = 30
3*10 = 30
etc.

Regarding the first approach (plugging in for the work being done by each machine), your numbers are correct. If each machine produces 2 units/day, then to complete the job in 9 days, 144/8 = 18 units must be produced each day. Since each machine produces 2 units/day, 9 total machines will be needed, so we'll need to add 3 machines -- the same answer that I got when I plugged in that each machine produces 1 unit/day.

Hope this helps!

(What exactly did you want to cross multiply?)

Turksonaaron wrote:Hi Mitch

I don't know why Inverse proportion really whips me to the core since high school. How do I attack this monster once and for all