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Serjik [45]
2 years ago
10

It takes Sue, Jeff and Todd 4 hours to paint a room together. If it takes Sue 10 hours by herself and Jeff 12 hours by himself,

how long would it take Todd to paint the room alone?
Mathematics
1 answer:
diamong [38]2 years ago
5 0

The number of time it would take Todd to paint the room alone is 15 hours.

  • Let the Todd's time be t.

<u>Given the following data:</u>

  • Combine time = 4 hours
  • Sue's time = 10 hours
  • Jeff's time = 12 hours

To calculate the number of time it would take Todd to paint the room alone:

How to solve a word problem:

In order to solve this exercise, we would first of all calculate their individual rate and combined rate respectively. Finally, we would add their individual rates together and equate it to the combined rate.

<u>For </u><u>Sue</u><u>:</u>

Rate = \frac{1}{10} \;work/hr

<u>For </u><u>Jeff</u><u>:</u>

Rate = \frac{1}{12} \;work/hr

<u>For </u><u>Todd</u><u>:</u>

Rate = \frac{1}{t} \;work/hr

<u>Combined rate:</u>

Rate = \frac{1}{4} \;work/hr

Adding the individual rates, we have:

\frac{1}{10} +\frac{1}{12} +\frac{1}{t} =\frac{1}{4} \\&#10;\\&#10;

Multiplying all through by 120t, we have:

12t+10t+120=30t\\&#10;\\&#10;22t+120=30t\\&#10;\\&#10;120=30t-22t\\&#10;\\&#10;120=8t\\&#10;\\&#10;t=\frac{120}{8}

t = 15 hours.

Read more on word problems here: brainly.com/question/13170908

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14 {x}^{10}  {y}^{7}

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3 years ago
Y = 4x – 18<br> y = -5x +9
adelina 88 [10]

Answer:

(3, -6)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
  • Terms/Coefficients
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Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = 4x - 18

y = -5x + 9

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em> [2nd Equation]:                                                                           4x - 18 = -5x + 9
  2. [Addition Property of Equality] Add 5x on both sides:                                   9x - 18 = 9
  3. [Addition Property of Equality] Add 18 on both sides:                                   9x = 27
  4. [Division Property of Equality] Divide 9 on both sides:                                  x = 3

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Substitute in <em>x</em> [1st Equation]:                                                                           y = 4(3) - 18
  2. Multiply:                                                                                                             y = 12 - 18
  3. Subtract:                                                                                                            y = -6
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tia_tia [17]

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