Work Rates and Fractions

The video tutorial explains how to solve a work rate problem involving Carlos and Destiny. Carlos can complete a job in 12 hours, and together with Destiny, they can finish it in 5 hours. The goal is to determine how long it would take Destiny to complete the job alone. The tutorial walks through setting up the problem, calculating individual and combined work rates, and solving the equation to find Destiny's time. The solution involves simplifying the equation and converting the result into a mixed number, concluding that Destiny takes 67 hours, or 8 and 4/7 hours, to complete the job alone.

If Carlos can complete a job in 12 hours, how much of the job does he complete in one hour?

• 1/12 of the job

• 1/5 of the job

• 1/10 of the job

• 1/15 of the job

When Carlos and Destiny work together, they complete the job in 5 hours. What is their combined work rate?

• 1/5 of the job per hour

• 1/15 of the job per hour

• 1/12 of the job per hour

• 1/10 of the job per hour

What equation is set up to find out how long Destiny takes to complete the job alone?

• 1/x + 1/5 = 1/12

• 1/12 + 1/x = 1/5

• 1/5 + 1/12 = 1/x

• 1/12 + 1/5 = 1/x

What does the equation 1/12 + 1/x = 1/5 represent in the context of the problem?

• The time it takes for Destiny to complete the job alone.

• The individual work rates of Carlos and Destiny.

• The combined work rate of Carlos and Destiny.

• The time it takes for Carlos to complete the job alone.

What is the least common denominator used to clear the fractions in the equation?

• 60x

• 60

• 12

• 5

After solving the equation, what is the time it takes for Destiny to complete the job alone?

• 67/7 hours

• 8 hours

• 5 hours

• 12 hours

What is the first step in solving the equation for Destiny's work rate?

• Multiply both sides by the least common denominator.

• Add the rates of Carlos and Destiny.

• Subtract Carlos's rate from the combined rate.

• Divide the combined rate by Carlos's rate.

Why is it necessary to clear fractions when solving the equation?

• To make the equation more complex.

• To increase the number of variables.

• To eliminate the need for a common denominator.

• To simplify the equation for easier calculation.

How is the improper fraction 67/7 converted into a mixed number?

• 9 and 3/7

• 6 and 6/7

• 8 and 4/7

• 7 and 5/7

What is the significance of the mixed number 8 and 4/7 in the context of the problem?

• It represents the time Destiny takes to complete the job alone.

• It represents the time Carlos takes to complete the job alone.

• It represents the time saved by working together.

• It represents the time they take together to complete the job.