Question

The number of hours required to do a job varies inversely as the number of people working. It takes 8 hours for 4 people to paint the inside of a house. How long would it take 5 peole to do the job?

Answer 1

Answer: it will take 5 people 6.4 hours to do the work.

Step-by-step explanation:

The number of hours required to do a job varies inversely as the number of people working. Let h represent the number of hours required to do the job. Let p represent the number of people working. Therefore,

h is inversely proportional to p

Introducing a constant of variation, k, it means that

h = k/p

It takes 8 hours for 4 people to paint the inside of a house. Therefore

8 = k/4

k = 8×4 = 32

The formula becomes

h = 32/p

To determine how many hours it will take 5 people to do the work, we will substitute p = 5 into the formula. It becomes

h = 32/5 = 6.4 hours