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zubka84 [21]
3 years ago
13

John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in 12 hours. If Rick works al

one, he can paint the room in 15 hours. Write an equation comparing the group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if working alone.
Mathematics
1 answer:
Tresset [83]3 years ago
4 0

Answer:

\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}

60 hours

Step-by-step explanation:

John - 12 hours

Rick - 15 hours

Molli - x hours

Together - 6 hours

Each of them can paint:

John - \frac{1}{12} of a room per hour

Rick - \frac{1}{15} of a room per hour

Molli - \frac{1}{x} of a room per hour

Together - \frac{1}{6} of a room per hour

So the equation is

\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}

Solve this equation:

\dfrac{1}{x}=\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{15}\\ \\\dfrac{1}{x}=\dfrac{10-5-4}{60}=\dfrac{1}{60}\\ \\x=60

Molli can paint the room in 60 hours.

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The given question is a quadratic equation and we can use several methods to get the solutions to this question. The solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

<h3>Quadratic Equation</h3>

Quadratic equation are polynomials with a second degree as it's highest power.

An example of a quadratic equation is

y = ax^2 + bx + c

The given quadratic equation is 24x^2 + 2x = 15

Let's rearrange the equation

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This implies that

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The equation or formula of quadratic formula is given as

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We can substitute the values into the equation and solve

y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-2 +- \sqrt{2^2 -4 * 24 * (-15)} }{2*24} \\y = \frac{-2+-\sqrt{4+1440} }{48} \\y = \frac{-2+-\sqrt{1444} }{48} \\y = \frac{-2+- 38}{48} \\y = \frac{-2+38}{48} \\y = \frac{3}{4}\\ \\or\\y = \frac{-2-38}{48} \\y = \frac{-40}{48} \\y = -\frac{5}{6}

From the calculations above, the solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

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