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katen-ka-za [31]
3 years ago
8

Rachael can paint a room in 9 hours. Kelsey can paint same room in 15 hours. How long if they paint it together.

Mathematics
2 answers:
Gwar [14]3 years ago
8 0

Rachael and Kelsey when work together will paint the room in 5.625 hours.

<u>Solution: </u>

Given that  

Rachael can paint a room in 9 hours.

Kelsey can paint same room in 15 hours.

Need to calculate number of hours to paint same room when both work together

Let say complete work of painting room be represented by w

Paint Work done by Rachael in 9 hours is complete work = w

So Paint Work done by Rachael in 1 hour = \frac{w}{9}

Paint Work done by Kelsey in 15 hours is complete work = w

So Paint Work done by Kelsey in 1 hour = \frac{w}{15}

Paint work done by Rachael and Kelsey together in 1 hour is given as:

=\frac{w}{9}+\frac{w}{15}=\frac{5 w+3 w}{45}=\frac{8 w}{45}

So number of hours required to complete work when both work together is given as:

=\frac{\text { Total work }}{\text { work done by them togther in } 1 \text { hour }}=\frac{w}{\left(\frac{8 w}{45}\right)}=5.625 \text { hours }

Hence Rachael and Kelsey when work together will paint the room in 5.625 hours.

ElenaW [278]3 years ago
7 0

Answer:

6 hours

Step-by-step explanation:

because if they work together it will be 9 hours slower than Kelsey's time alone.

not sure if correct

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The perimeter of a rectangle is equal to 163 yard. The width is 8 more than twice the length. Find the length and width.​
Sedaia [141]

Answer:

l = 29.4 yards

w = 66.8 yards

General Formulas and Concepts:

  • Order of Operations: BPEMDAS
  • Perimeter of a Rectangle: P = 2w + 2l

Step-by-step explanation:

<u>Step 1: Define</u>

P = 163 yards

w = 2l + 8

l = l

<u>Step 2: Set up equation</u>

P = 2w + 2l

163 = 2(2l + 8) + l

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

  1. Distribute 2:                              163 = 4l + 16 + l
  2. Combine like terms:                 163 = 5l + 16
  3. Subtract 16 on both sides:        147 = 5l
  4. Divide both sides by 5:             147/5 = l
  5. Rewrite:                                      l = 147/5
  6. Evaluate:                                    l = 29.4 yards

<u>Step 4: Find </u><em><u>w</u></em>

  1. Define:                    w = 2l + 8
  2. Substitute:              w = 2(29.4) + 8
  3. Multiply:                  w = 58.8 + 8
  4. Add:                        w = 66.8 yards
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3 years ago
Plot the vertices (-2, -8), (-2, 2), and (8, 2).
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Answer:

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Step-by-step explanation:

The diagonals of a rectangle have the same midpoint, so for points A, B, C, D, we must have ...

  (A+C)/2 = (B+D)/2

  D = A + C - B

  D = (-2, -8) +(8, 2) -(-2, 2) = (-2+8+2, -8+2-2)

  D = (8, -8)

__

The side lengths are 2-(-8) = 10, and 8-(-2) = 10. The area is the product of the side lengths, so is 10×10 = 100 square units.

_____

<em>Comment on side lengths</em>

When the end points of one side are on the same vertical line, the length of that side is the difference of y-coordinates. When the points lie on the same horizontal line, the side length is the difference of x-coordinates.

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Read 2 more answers
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