Inverse Variation and Job Completion

The video tutorial explains how the time required to complete a job varies inversely with the number of workers. It uses an example where eight workers complete a job in six hours to derive the inverse variation equation T = K/P. The variation constant K is calculated as 48. The tutorial then determines how long it would take for nine workers to complete the same job, resulting in 5.3 repeating hours or 5 hours and 20 minutes. Various ways to express the answer are discussed, highlighting the impact of adding an extra worker.

What does it mean when time varies inversely with the number of workers?

• Time increases as the number of workers increases.

• Time remains constant regardless of the number of workers.

• Time and number of workers are unrelated.

• Time decreases as the number of workers increases.

What is the general form of an inverse variation equation?

• Y = K + X

• Y = K / X

• Y = X / K

• Y = K * X

Tags

CCSS.HSF-LE.A.1B

In the context of the problem, what does the variable K represent?

• The variation constant.

• The total time taken to complete the job.

• The number of jobs completed.

• The total number of workers.

Tags

CCSS.HSF-LE.A.1B

How do you calculate the variation constant K using the given values?

• Subtract the number of workers from the time.

• Divide the time by the number of workers.

• Multiply the time by the number of workers.

• Add the time and number of workers.

Tags

CCSS.HSF-LE.A.1B

What is the equation used to find the time required with a different number of workers?

• T = 48 * P

• T = 48 + P

• T = 48 / P

• T = P / 48

Tags

CCSS.HSA.CED.A.1

How long does it take for 9 workers to complete the job?

• 7 hours

• 4.5 hours

• 5.3 hours

• 6 hours

What is the decimal representation of 5 and 1/3 hours?

• 5.333

• 5.33

• 5.3333

• 5.3

Tags

CCSS.4.NF.C.6

How can 5 and 1/3 hours be expressed in hours and minutes?

• 5 hours 20 minutes

• 5 hours 15 minutes

• 5 hours 25 minutes

• 5 hours 30 minutes

Tags

CCSS.8.EE.C.7B

What is the impact of adding one more worker to the team?

• The job takes 10 minutes less.

• The job takes 20 minutes more.

• The job takes 40 minutes less.

• The job takes 1 hour longer.

Tags

CCSS.RI.7.3

CCSS.RI.7.5

CCSS.RI.8.3

CCSS.RI.8.5

CCSS.RI.9-10.3

Why might it be useful to express time in hours and minutes?

• To make it easier to calculate costs.

• To align with standard timekeeping practices.

• To avoid using decimals.

• To simplify the equation.

Tags

CCSS.RI.7.3

CCSS.RI.8.3

CCSS.RI.8.5

CCSS.RI.9-10.3

CCSS.RI.9-10.5