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19 February, 02:47

2 women and 7 girls can do a peice of work in 4 days. 4 women and 4 girls can do the same work in 3 days. How long would it take for 1 women and 1 girl to do the work.

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  1. 19 February, 02:50
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    x: work a woman can do in 1 day

    y: work a girl can do in 1 day

    Then

    2x + 7y = 1/4

    4x + 4y = 1/3

    4x + 14y = 2/4 (1)

    4x + 4y = 1/3 (2)

    => Let (1) - (2), 10y = 2/4-1/3 10y = 1/6 y = 1 / (6x10) = 1/60 (work)

    => From (2),4x = 1/3 - 4x1/60 = > 4x = 16/60 = > x = 4/60 (work)

    => 1 day, a woman and a girl can do: 1/60+4/60 = 5/60 = 1/12 (work)

    Then, the day required for a woman and a girl to complete work: 12 days
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