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7 November, 00:07

It takes a painter and his friend 12 hours to paint a room. If the painter was working alone, it would take him 18 hours less than if his friend was working alone. How long does it take the painter to paint the room by himself?

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Answers (2)
  1. 7 November, 01:31
    0
    18 hours

    Step-by-step explanation:

    Combined time = (T1 * T2 / (T1 + T2)

    Let x be the time friend takes

    12 = [x (x - 18) ]/[x + x - 18]

    12 (2x - 18) = x² - 18x

    24x - 216 = x² - 18x

    x² - 42x + 216 = 0

    x² - 6x - 36x + 216 = 0

    x (x - 6) - 36 (x - 6) = 0

    (x - : 6) (x - 36) = 0

    x = 6, 36

    His time:

    x - 18

    6 - 18 = - 12 (not possible)

    36 - 18 = 18 hours
  2. 7 November, 02:24
    0
    18 hours

    Step-by-step explanation:

    The equation for time working is

    1/a + 1/b = 1/c

    where a and b are the times working alone and c is the time working together

    1/b-18 + 1/b = 1/12

    Multiply by 12b (b-18) to clear the fractions

    12b (b-18) * (1/b-18 + 1/b) = 1/12 * 12b (b-18)

    12b + 12 (b-18) = b (b-18)

    Distribute

    12b + 12b - 216 = b^2-18b

    Combine like terms

    24b-216=b^2-18b

    Subtract 24b from each side

    24b-24b - 216 = b^2 - 18b-24b

    -216 = b^2 - 42b

    Add 216 to each side

    0 = b^2 - 42b + 216

    Factor

    0 = (b-36) (b-6)

    b = 36

    b=6 is not possible since this is less time then when they worked together

    Using the zero product property

    The painter takes b-18 = 36-18 = 18 hours

    The friend takes 36 hours

    b=36 b=6
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