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A works 6 days and B works 8 days to finish a job. Alternatively A works 4 days and B 12 days. How long would A take alone?

Class 10Work Rates with Two UnknownsAlgebra — Systems of Equations

A20 days
B12 days
C8 days
D10 days

Step-by-Step Solution

6 a + 8 b = 1, 4 a + 12 b = 1

. Multiply the first by 2 and the second by 3:

12 a + 16 b = 2, 12 a + 36 b = 3

, so

b = \frac{1}{20}

, then

a = \frac{1}{10}

.

Answer: D) 10 days

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