Question 958724
this looks like it can be solved with an inverse ratio.


inverse ratio formula is y = k / x


first you find k.


then you use k to find your solution.


let y = days and x equal number of machines.


when y = 105 and x = 15, you get 105 = k / 15.


solve for k to get k = 105 * 15 = 1575


that's your constant of variation.


that remains the same.


when x = 35, the equation becomes y = 1575 / 35.


solve for y to get y = 45.


with 15 machines running, it takes 105 days.


with 35 machines running, it takes 45 days.


you could also solve this by using the rate per machine * number of machines * time = quantity formula.


let quantity equal 1 job.
let number of machines = 15
let time = 105 days.


formula becomes:


rate per machine * 15 * 105 days = 1


solve for rate per machine to get rate per machine = 1 / (15 * 105).


rate per machine is equal to 1 / (15 * 105) of the job completed in one day.


how many days would it take 35 machines to do the job?


number of machines is now 35.
rate per machine is still 1 / (15 * 105).
quantity is still 1.


formula becomes:


35 * 1 / (15 * 105) * number of days = 1


solve for number of days to get:


number of days = (1 * 15 * 105) / 35 which is equal to 45 days.


both formulas get you the same answer.


the inverse ratio formula is y = k / x.


the number of machines * rate of each machine * time = quantity formula can be shown as:


r * m * t = q


r = rate per machine
m = number of machines
t = time
q = quantity of work.