SOLUTION: if 15 machines do the work in 105 days then how many days are required for same work by 35 machines?

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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