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6 November, 13:06

Larry and Curly can build a bookcase together in $2$ hours. Curly and Moe can build a bookcase together in $1 / frac{2}{3}$ hours. Larry, Curly, and Moe can build a bookcase together in $1$ hour. How many hours would it take for Larry and Moe to build a bookcase together?

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  1. 6 November, 13:31
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    1 ¹/₉ hours

    Step-by-step explanation:

    Let's say L is Larry's speed, C is Curly's speed, and M is Moe's speed.

    1 = 2 (L + C)

    1 = 1 ⅔ (C + M)

    1 = 1 (L + C + M)

    Solve the system of equations. First, simplify the equations:

    1 = 2L + 2C

    3 = 5C + 5M

    1 = L + C + M

    Double the third equation and subtract the first equation from it:

    2 = 2L + 2C + 2M

    1 = 2L + 2C

    1 = 2M

    M = 1/2

    Plugging into the second and third equations, we get:

    C = 1/10

    L = 2/5

    Therefore, the time it takes Larry and Moe together is:

    1 = t (L + M)

    t = 1 / (L + M)

    t = 1 / (2/5 + 1/2)

    t = 1 / (4/10 + 5/10)

    t = 1 / (9/10)

    t = 10/9

    t = 1 ¹/₉ hours

    It takes them 1 ¹/₉ hours, or 1 hour 6 minutes 40 seconds.
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