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 4?
1/4 the machines, so 4 times as long
The real question is -- how can six machines be decreased by a factor of 4?
Step 1: Find the rate at which one machine works.
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.
To solve this problem, we can use the concept of machine-hours, which is a measure of work completed by a machine in an hour. Let's denote the number of machine-hours required to complete the order as X.
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.