Working simultaneously

Plug in numbers for this problem.

Let x = 24

therefore, 4 machines produce 24 units in 6 days, that gives us 4 units per day for 6 days.

Case 1 -
Machines -> 4, Units -> 24, Days -> 6

Case 2 -
Machines -> M, Units -> 72 (remember 3x), Days -> 4

M = 72 / 4 -> M = 18

18 machines can produce 72 units in 4 days.

Total work by 4 machines in 1 day - (1/6 + 1/6 + 1/6 + 1/6) x = 2/3 x

total work to be done - 3x, by 4 machines in 1 day = 9x /2x = 4.5 units

no of machines reuqured to do 3x work in 4 days = 4.5 x 4 = 18

4 machines--x units--6 days

4 machines--how many units?--4 days

how many units=y

y=4x/6=2x/3


how many machines--3x units--4 days

how many machines=z

z=12x/y=12x/(2x/3)=18

Hey this problem takes only 45 sec. Formula : amount = rate * work done
Given R1=R2:

step 1 : X= R1 * (4Machines * 6 days)
step 2 : 3X = R2* ( Y machines * 4 days )
step 3 : equate R1= R2
ie.. X/(4*6) = 3X/ (Y * 4)
Y = 18...

Hope you got it...........

Simpler way ( I think )

4 machines do some work in 6 days
1 machine does it in 24 days.

24 days are needed to do some work by 1 machine
To do it in 4 days, we shall need : 6 machines.

To do thrice the work in 4 days, we shall need 18 machines.

I think the part where x and 3c comes in ( adding the 3rd variable ) simply kicks us in the head and confuses us. Essentially, its the same rate/work problems we've been doing in our heads all day long

ska7945 wrote: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?

A. 24
B. 18
C. 16
D. 12
E. 8

We are given that 4 machines can complete x units in 6 days. Thus, the rate of the 4 machines is x/6.
Next we need to determine the number of machines needed to produce a rate of 3x/4. To calculate that number of machines, we can use the following proportion in which the value in each numerator is the number of machines and the value in each denominator is the corresponding rate of those machines. We can let n = the number of machines needed:

4/(x/6) = n/(3x/4)

24/x = 4n/3x

72x = 4nx

18 = n

Answer: B