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2 men and 3 women finish a job in 10 days; 3 men and 2 women finish it in 8 days. How long will 2 men and 1 woman take?

Competition practiceTime & Work / Pipes

A10 days
B14 days
C12 1/2 days
D11 1/9 days

Step-by-Step Solution

2 m + 3 w = \frac{1}{10}, 3 m + 2 w = \frac{1}{8}

. Adding:

m + w = \frac{9}{200}

; subtracting:

m - w = \frac{5}{200}

. So

m = \frac{7}{200}, w = \frac{2}{200} .2 m + w = \frac{16}{200} = \frac{2}{25}

.

Answer: C) 12 1/2 days

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