1/4 the machines, so 4 times as long
The real question is -- how can six machines be decreased by a factor of 4?
The real question is -- how can six machines be decreased by a factor of 4?
Since six machines can complete the order in 22 hours, the rate at which one machine works is 22 * 6 = 132 hours per machine.
Step 2: Calculate the number of machines after decreasing by a factor of 4.
Since the number of working machines decreased by a factor of 4, there would be 6 / 4 = 1.5 machines.
Step 3: Round the number of machines down to the nearest whole number.
As we can't have a fraction of a machine, we need to round down to get the nearest whole number. Therefore, there would be 1 machine working.
Step 4: Calculate the time needed to fill the order with 1 machine.
Since one machine works at a rate of 132 hours per machine, it would take 132 * 1 = 132 hours to fill the order with 1 machine.
Therefore, it would take 132 hours to fill the order if the number of working machines decreased by a factor of 4.
We are given that when six machines work together, they can complete the order in 22 hours. This means that the total machine-hours required to complete the order is 22*X.
If the number of working machines decreases by a factor of 4, then only (6/4) = 1.5 machines will be working. Multiplying this by the time it takes to complete the order with 6 machines gives us the time it will take with 1.5 machines.
Therefore, the number of machine-hours required when 1.5 machines are working is (22*X) * (6/1.5) = 88*X.
Since we want to find the time it takes to fill the order when the number of machines decreases by a factor of 4, we can set up the equation:
88*X = X
Simplifying this equation, we get:
88 = 1
Dividing both sides by X gives us:
88 = 1
So, it will take 88 hours to fill the order when the number of working machines decreases by a factor of 4.