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?
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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
=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.
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. :)
2 Explanations