The time it takes a home building company to build a new home is directly proportional to the size of the home and inversely proportional to the number of people on the building crew. If it takes 10 workers 4 weeks to build a 2,000 square foot home, how long will it take 6 workers to build the home?

Solution:

Let t = time it takes to build a home

w = number of workers

s = size of home

The joint variation between these variables can be represented by

t = ks/w

Substitute 4 for t, 2000 for s and 10 for w and solve for k.

4 = k(2000)/10

Multiply both sides by 10 to clear the denominator.

40 = k(2000)

Divide by 2000 to get

40/2000 = 1/50 = k.

Now substitute 6 for w, 2000 for s and 1/50 for k and solve for t.

t = (1/50)(2000/6)

t = 2000/300, t = 6.66. Therefore, it takes 6 workers 6 2/3 weeks to build a 2,000 square foot home.