Question

It takes 10 workers 24 hours to do a job. How does y vary with x − directly or inversely? What is the coefficient of variation?

Answer 1

The total cost y varies directly with the number of hours x needed to complete a job, with a direct variation coefficient of 100.

Step-by-step explanation:

When analyzing the variation between two variables, specifically how y varies with x, we consider whether the relationship is direct or inverse. In the scenario provided, where it takes 10 workers 24 hours to do a job, if we let x represent the number of hours it takes to get the job done and y represent the total cost to the customer, we can establish that as the number of hours increases, the total cost also increases, assuming workers are paid by the hour. This suggests a direct variation.

Given that widget workers receive $10 per hour, the cost y to the customer for x hours of work would be 10 workers × $10 per hour × x hours. So, y = 10 × 10 × x = 100x. Hence, the relationship between y and x is directly proportional with a coefficient of variation of 100.