Answer : 7.5 hours.
Step-by-step explanation:
We can use the principle of direct proportionality to determine how long it would take four machines to produce the same number of DVDs if five machines could produce 1000 DVDs in six hours.
The variables need to be defined:
- Let this be the amount of time it takes for four machines to make one thousand DVDs.
Suppose that k is the proportionality constant.
We realize that the quantity of machines and the time are contrarily corresponding, so we can compose:
We can simplify the equation by dividing 5 machines by 6 hours to get 4 machines by t hours to get k.
We can now use k to determine the value of t when four machines are utilized: k = 5 machines less than 6 hours / (4 machines less than t hours) k = 15 / (2t).
4 machines x t hours equals 5 machines x 6 hours / k 4 machines x t hours equals 5 machines x 6 hours (2t) / 15 4t = 4t. Accordingly, it would take 4 machines to produce 1000 DVDs in the following amount of time:
5 machines × 6 hours/(4 machines) = 7.5 hours
So 4 machines would require 7.5 hours to create 1000 DVDs.