Problem Solving

Six machines working at the same constant rate, together can complete a certain jos in 12 days. How many aditional machines, each working at the same constant rate,will be needed to complete a job in 8 days?

Does anyone know how the answer to this question and how to get it?

Thanks

Approach 1:

When the job is undefined, we can plug in our own number for the job.

Let's say each machine produces one unit each day. Then the 6 machines together would produce 6 units each day. Over 12 days, 6 * 12 = 72 units would be produced.

If we want to produce the 72 units in only 8 days, we'll need 72/8 = 9 units to be produced each day.

Since we'll need 3 more units to be produced each day, and each machine produces 1 unit per day, we'll need 3 more machines.

The correct answer is B.

Approach 2:

(number of machines) x (number of days) always has to yield the same amount of work.

So we could set up this equation:

(number of machines) x (number of days) = (number of machines) x (number of days)

6 * 12 = x * 8
72 = 8x
x = 9

Since we'll need 9 machines altogether, and we currently have 6, we'll need 9-6=3 more machines.

In math terms, the number of machines is inversely proportional to the number of days. When two values are inversely proportional, as one value goes up, the other must go down, so that the product of the two values is always the same. So in the problem above, as the number of machines goes up, the number of days must go down, so that we're always getting the same amount of work done

thank your for your help, I get it now