Question

if it takes 10 minutes for 15 machines to make 5 widgets, how many minutes would it take 5 machines to make 15 widgets

Answer 1

The number of minutes it will take 5 machines to make 15 widgets is 90 minutes

Given that :

The time taken to make a widget is directly proportional to the number of widgets made and inversely proportional to the number of machines utilized.

Using the variation protocol defined :

Let :

n = number of widgets made

n = number of widgets made m = number of machines used

n = number of widgets made m = number of machines used t = time taken

Hence, from joint variation :

t α n α 1/m

t = kn/m

Where k = constant of proportionality :

Solving for k

When t = 10, n = 5, m = 15

10 = (k × 5) / 15

15 × 10 = 5k

150 = 5k

k = 150 / 5

k = 30

Equation becomes :

t = 30n/m

Solve for t ;

When m = 5 ; n = 15

t = (30 × 15) / 5

5t = 450

t = 450 / 5

t = 90

Hence, it will take 90 minutes.

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