Question

the time it takes to finish a job varies inversely as the number of workers helping with the job. if 8 workers require 12 hours to finish a job how much time would 18 workers require to finish the same job

Answer 1

To solve this problem, we can use the concept of inverse variation. Inverse variation states that when two variables are inversely proportional, their product remains constant. Using the equation w * t = k, we can determine the time required when 18 workers are helping with the job.

Step-by-step explanation:

To solve this problem, we can use the concept of inverse variation. Inverse variation states that when two variables are inversely proportional, their product remains constant.

Let's represent the number of workers as w and the time taken to finish the job as t. We are given that 8 workers require 12 hours to finish the job, so we have the equation:

w * t = k

Substituting the given values, we get:

(8 * 12) = k

k = 96

Now, we can find the time required when 18 workers are helping with the job. Let's substitute the values in the equation:

(18 * t) = 96

t = 96 / 18

t ≈ 5.33

Therefore, it would take approximately 5.33 hours for 18 workers to finish the same job.