Painting Rates and Combined Work

The video tutorial explains how to solve a problem involving Rhea and Destiny painting a room together. It highlights a common mistake of simply averaging their individual times and provides a correct method by calculating their rates and setting up an equation. The solution involves finding the least common multiple to clear fractions and solving for the time it takes them to paint the room together, which is 2.4 hours.

What is a common mistake when calculating the time it takes for Rhea and Destiny to paint the room together?

• Averaging their rates

• Adding their individual times and dividing by two

• Multiplying their individual times

• Subtracting Destiny's time from Rhea's time

Tags

CCSS.HSA.CED.A.1

How long does it take Rhea to paint the room by herself?

• 3 hours

• 5 hours

• 4 hours

• 6 hours

Tags

CCSS.HSA.CED.A.1

Why is the incorrect answer of 5 hours not logical?

• Because it is the average of their rates

• Because Rhea can paint the room alone in less time

• Because Destiny can paint the room alone in less time

• Because it is the sum of their rates

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

What is Rhea's painting rate per hour?

• 1/6 of the room

• 1/4 of the room

• 1/3 of the room

• 1/5 of the room

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

What is Destiny's painting rate per hour?

• 1/6 of the room

• 1/5 of the room

• 1/4 of the room

• 1/3 of the room

What equation represents the combined effort of Rhea and Destiny to paint the room?

• T/6 - T/4 = 1

• T/6 + T/4 = 1

• T/4 + T/6 = 1

• T/4 - T/6 = 1

Tags

CCSS.8.EE.C.7B

What does the number 1 represent in the equation T/4 + T/6 = 1?

• One hour of work

• One half of the room painted

• One painter working

• One complete room painted

What is the least common multiple of 4 and 6 used to clear the fractions in the equation?

• 24

• 12

• 18

• 6

Tags

CCSS.8.EE.C.7B

After clearing the fractions, what does the equation simplify to?

• 6T = 12

• 4T = 12

• 3T + 2T = 12

• 5T = 12

Tags

CCSS.HSA.CED.A.1

What is the final solution for the time it takes Rhea and Destiny to paint the room together?

• 3 hours

• 2.4 hours

• 2 hours

• 2.5 hours

Tags

CCSS.HSA.CED.A.1