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4 men and 2 boys finish a job in 6 days; 1 man and 4 boys finish it in 10 days. How long would 1 man take alone?

Class 10Work Rates with Two UnknownsAlgebra — Systems of Equations

A60 days
B30 days
C24 days
D40 days

Step-by-Step Solution

4 m + 2 b = \frac{1}{6}, m + 4 b = \frac{1}{10}

. Multiply the second by 4 and subtract:

14 b = \frac{2}{5} - \frac{1}{6} = \frac{7}{30}

, so

b = \frac{1}{60}

and

m = \frac{1}{10} - \frac{4}{60} = \frac{1}{30}

.

Answer: B) 30 days

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