Question

if 9 men and 12 women can do a piece of work in 4 days and 4 men and 16 women can do the same piece of work in 6 days.how long will 6 men and 24 women take to complete the same work?

Answer 1

Form the expressions:

9 Men and 12 women do the work in 4 days:

9M + 12W = 4D

4 men and 16 women do the work in 6 days:

4M + 16W = 6D

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Form the equations:

9M + 12W = 4D ------------------ [ 1 ]

4M + 16W = 6D ------------------ [ 2 ]

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Since the work is the same:

(9 x 4)M + (12 x 4)W = (4 x 6)M + (16 x 6)W

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Simplify and find M in term of W:

36M + 48W = 24M + 96W

36M - 24M = 96W - 48W

12M = 48W

1M = 4 W ------------------ [ 3 ]

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Substitute 1M = 4W into [1] to find W:

9M + 12W = 4D

(9 x 4) W + 12W = 4D

36W + 12W = 4D

48W = 4D

1W = 4/48 D

1W = 1/12 D

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Substitute 1W = 1/12D into [3] to find M:

1M = 4 W

1M = 4/12

1M = 1/3 D

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$\boxed { \text {Now we know that 1W = 1/12 D and 1M = 1/3 D}}$

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Now find the days needed for 6 Men and 24 Women:

6M + 24W

= 6(1/3) + 24 (1/2)

= 2 + 2 = 4 days

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Answer: 6 Men and 24 Women will need 4 days