Working simultaneously and independently at an identical constant

Working simultaneously and independently at an identical constant rate, four 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?

2 Explanations

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AMURE ADENIYI BOLAJI COLLINS

4m =x/6 machine days.
I machine = x/(4*6)
therefore, 4 machine =4* x/(24*3)
then = 1/18 =
18

Nov 28, 2016 • Comment

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Jeffrey Braganza

=4*(6/4)*(3x/x) = 18
multiply by (8/4), because no of days reduced from 8 to 4, so to do the same work in lesser days, more machines will be required.
multiply by (3x/x), because the no of units required has gone up from x to 3x, hence more machines will be required to complete this task.

Jan 2, 2016 • Comment

marina kawai

I don't understand it, please explain it from beginning for me.
thank you

Jun 11, 2017 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Marina,

I'm happy to help :) First, let's consider the work formula:

work = rate * time

In this problem, let's call the rate at which 1 machine can make a product R, where R has units products/days. Also, "work" in this case is expressed in # of products.

So, given the information in the prompt,

x = 4R*6

The rate of 4 machines is simply 4 multiplied by R, the rate of one machine. And in the equation above, x is the number of products produced, while 6 is the number of days it takes 4 machines to make x products.

Let's solve for R:

x = 4R*(6 days)
x = 24R
x/24 = R

Now that we've solved for the rate of one machine, we can use that value to find the number of machines it takes to make 3x products in 4 days:

3x = n*R*(4days)
3x = n*(x/24)*4days

where n is the number of machines.

Solving for n, we see that

3x = n*x/6
3 = n/6
18 = n

So, it would take 18 machines to make 3x products in 4 days. :)

Jun 21, 2017 • Reply