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Question 958724: if 15 machines do the work in 105 days then how many days are required for same work by 35 machines?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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