All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours. How many hours would it take to fill the order if the number of working machines decreased by factor of 2?
half as many machines, so twice as long: 44 hrs
44 hrs.....bc it is half as many so 22x2...
44 hours, By timing 22 by 2 since its half
44hours, because if we have half as many machines, then we need twice as long.
So basically, "factor of 2" doesn't literally mean 2. It's not 6-2=4 machines, it's 6/2=3 machines. Now since it decreased, we now have half as many machines. So this means, the machines need twice as long to finish the job. To find that time you simply multiply 22 by 2 as shown below:
6/2 = 3 machines
It takes 22 hours for 6 machines to finish.
22x2=44
Answer: 44 hours
To solve this problem, we can use the concept of "work rates". Let's denote the number of machines as 'n' and the time it takes to complete the order as 't'.
We know that when 6 machines are working together, they can finish the big order in 22 hours. This means that the combined work rate of these machines is equal to the work required to complete the order divided by the time taken:
Work rate of 6 machines = Order size / Time taken = 1/22
Since all the machines work at the same rate, the work rate of a single machine can be calculated by dividing the work rate of 6 machines by 6:
Work rate of 1 machine = Work rate of 6 machines / 6 = 1/132
Now, we need to find the time it would take to fill the order if the number of working machines decreased by a factor of 2. Let's denote this number as 'n_new'. From the given information, we know that:
n_new = n / 2
Using the work rate formula, we can express the time taken with the new number of machines working:
Time taken with n_new machines = Order size / Work rate of n_new machines
Substituting the value of 'n_new', we have:
Time taken with n/2 machines = Order size / (Work rate of 1 machine * (n/2))
Time taken with n/2 machines = Order size / (1/132 * (n/2))
Simplifying further:
Time taken with n/2 machines = Order size / (n/264)
Time taken with n/2 machines = Order size * (264/n)
Therefore, the time taken to fill the order with the new number of working machines is given by:
t_new = t * (264/n)
Since we know that it takes 22 hours to complete the order with 6 machines, we can plug in these values:
t_new = 22 * (264/6)
Simplifying further:
t_new = 22 * 44
t_new = 968
Hence, it would take 968 hours to fill the order if the number of working machines decreased by a factor of 2.
11 hours
This is because it is saying decreased and not increased. So we will have to divide 22 by 2 and that equals 11 hours.