Question on combined work rates

[stephkhaira]

6 machines work at the same constant rate and it takes them 12 days to complete 1 job. If the job must be done in 8 days, how many machines should be added?

2
3
4
6
8


[spoiler]ans: 3[/spoiler]

[Brent@GMATPrepNow]

6 machines work at the same constant rate and it takes them 12 days to complete 1 job. If the job must be done in 8 days, how many machines should be added?

2
3
4
6
8

[spoiler]ans: 3[/spoiler]

If 6 machines take 12 days to complete the job, then we can say that the job takes 72 "machine days" to complete the job (6 x 12 = 72)

To complete the job in 8 days would require 9 machines (72 machine days divided by 8)

So, we need an additional 3 machines.

Cheers,
Brent

[GMATGuruNY]

6 machines work at the same constant rate and it takes them 12 days to complete 1 job. If the job must be done in 8 days, how many machines should be added?

2
3
4
6
8


[spoiler]ans: 3[/spoiler]

Let the rate for each machine = 1 unit per day.
Rate for 6 machines = 6 units per day.
In 12 days, the amount of work produced = r*t = 6*12 = 72 units.
To produce 72 units in 8 days, the required amount of work per day = w/t = 72/8 = 9 units per day.
To increase the rate from 6 units per day to 9 units per day, 3 more machines are needed.

The correct answer is B.

[[email protected]]

Hi stephkhaira,

This work formula question is rather similar to the other one that you posted (and both Brent and Mitch's explanations are easy ways to answer this question worth knowing). The ratio pattern I noted in the other question is also available here; it's just that the numbers are different, so the ratio is different.

Here, the number of days decreases from 12 to 8, which is a 33 1/3% decrease. To offset that decrease, and end up with the same result, the other variable (in this case, the total number of machines) must increase by 50%

We started with 6 machines; a 50% increase is 6 + 3 = 9 total machines.

Since the question asked for the total machines that would be ADDED, the answer is 3.

GMAT assassins aren't born, they're made,
Rich