Quadratic Equations and Rates Problems

The video tutorial explains how to determine the time it takes for Skylar to paint a room alone if Ermius is unavailable. It starts by establishing the combined rate of Skylar and Ermius working together, then calculates their individual rates. A rational equation is set up and solved using the quadratic formula to find Skylar's time, which is approximately 13.88 hours.

How long does it take for Skylar and Ermius to paint the room together?

• 8 hours

• 5 hours

• 12 hours

• 10 hours

If Ermius works alone, how many more hours does it take him compared to Skylar?

• 3 hours

• 4 hours

• 5 hours

• 6 hours

What is Skylar's rate of painting the room per hour if it takes him T hours?

• T/5 of the room per hour

• T rooms per hour

• 1/T of the room per hour

• 5/T of the room per hour

What equation represents the sum of Skylar and Ermius's rates?

• 1/T + 1/(T+5) = 1/5

• 1/T + 1/(T+5) = 1/8

• 1/T + 1/(T+5) = 1/10

• 1/T + 1/(T+5) = 1/12

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

• 8(T+5)

• 8T(T+5)

• 8T

• T(T+5)

What type of equation is formed after clearing the fractions?

• Linear equation

• Exponential equation

• Quadratic equation

• Cubic equation

Which formula is used to solve the quadratic equation in this problem?

• Binomial theorem

• Factorial formula

• Quadratic formula

• Pythagorean theorem

What are the values of A, B, and C in the quadratic equation?

• A=1, B=-11, C=-40

• A=1, B=11, C=40

• A=1, B=-11, C=40

• A=1, B=11, C=-40

What is the approximate time it takes Skylar to paint the room alone?

• 10.88 hours

• 11.88 hours

• 13.88 hours

• 12.88 hours

Why is T sub 2 excluded as a solution?

• It is not an integer

• It is not a real number

• It is too large

• It is negative