rates

[yvonne12]

I want to know if I did this right.

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

ans 3
6/x = x/8 cross multiply and get 3

is this correct?

[jayhawk2001]

Use the standard rate-formula to solve this

6 machines complete the job in 12 days, so
6 * 1/x = 1/12, so x = 72

n additional machines complete the job in 8 days
(n+6) * 1/72 = 1/8

So, n = 3

[Scott@TargetTestPrep]

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

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

6/(1/12) = x/(1/8)

72 = 8x

x = 9

So we need 9 - 6 = 3 more machines.

Answer: 3