# Can someone help? Gmat question!

#### Ruthiea22

##### New member
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines working simultaneously and independently at this constant rate can produce a total of 3x units of product P in 4 days!

#### skeeter

##### Elite Member
4 machines produce x units in 6 days $$\displaystyle \implies$$ 1 machine produces x/4 units in 6 days $$\displaystyle \implies$$ 1 machine produces x units in 24 days.

Let n be the number of machines ...

$$\displaystyle n \cdot \dfrac{x}{24} = \dfrac{3x}{4}$$

#### Dr.Peterson

##### Elite Member
Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines working simultaneously and independently at this constant rate can produce a total of 3x units of product P in 4 days!
You could just count machine-days. How many does it take to produce x units? How many does it take to produce 3x units? How many machines will do that many machine-days of work in 4 days?

#### Ruthiea22

##### New member
4 machines produce x units in 6 days $$\displaystyle \implies$$ 1 machine produces x/4 units in 6 days $$\displaystyle \implies$$ 1 machine produces x units in 24 days.

Let n be the number of machines ...

$$\displaystyle n \cdot \dfrac{x}{24} = \dfrac{3x}{4}$$
Hi Skeeter! Can you finish the problem?

#### Dr.Peterson

##### Elite Member
Hi Skeeter! Can you finish the problem?

We prefer to work with you, rather than do the work for you, because you learn better that way.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi Skeeter! Can you finish the problem?
It seems that you are saying that you could not proceed further beyond skeeters response. Let us try to help by digging a little deeper

What did the problem ask you to find?

Please tell us the variables that skeeter has used in that equation (including the definitions connecting those to the problem).

Please tell us exactly where you are stuck?

#### Ruthiea22

##### New member
n.x/24=3x/24
This is the equation skeeter gave me!

#### Ruthiea22

##### New member
Working simultaneously and independently at an identical constant rate 4 machines of a certain type can produce a total of x units of product P in 6 days! How many of these machines working simultaneously and independently at this constant rate can produce a total of 3x units of product P in 4 days? This is the question being asked! Skeeter didn’t finish explaining the problem so I don’t know how to calculate the number of machines it took to produce 3x units of product P in 4 days. Please help!

#### Subhotosh Khan

##### Super Moderator
Staff member
n.x/24=3x/24
This is the equation skeeter gave me!
What does 'n' stand for in the equation above?

Starting in the begining, without looking at response #2,

can you re-derive Skeeter's equation?

#### Ruthiea22

##### New member
n is the number of machines!

#### Subhotosh Khan

##### Super Moderator
Staff member
n is the number of machines!
Correct.

Can you re-derive skeeter's equation - from your original post? Before doing that study response #2 (made by skeeter) carefully - making sure you understand each step. If you do not understand any step - tell exactly where you are stuck.