Inverse Variation (Word Problems)

Question

When building a house, the number of days required to build is inversely proportional to with the number of workers. One house was built in 36 days by 27 workers. How many days would it take to build a similar house with 9 workers?

Answer 1

Let d = number of days

Let w = number of workers

For inverse variation d = k/w or dw = k

As one variable goes up the other goes down

k = dw = 36x27 = 972

d = 972/9 = 108

It will take 108 days to build the house with 9 workers.

This should make perfect sense. We are now using only one-third of the numbers of workers so it will take 3 times longer to build the house.