Bunuel wrote:

A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?

A. \(3 \frac{3}{7}\)

B. \(6 \frac{6}{7}\)

C. \(7\)

D. \(7 \frac{23}{35}\)

E. \(7 \frac{6}{7}\)

We can let a = the number of days A will complete the job alone, b = the number of days B will complete the job alone and c = the number of days C will complete the job alone. We can now create the following combined rate equations:

1/a + 1/b = 1/10

and

1/b + 1/c = 1/15

and

1/a + 1/c = 1/8

Adding the equations together, we have:

2/a + 2/b + 2/c = 1/10 + 1/15 + 1/8

2/a + 2/b + 2/c = 12/120 + 8/120 + 15/120

2/a + 2/b + 2/c = 35/120= 7/24

Thus, 1/a + 1/b + 1/c = 7/24 x 1/2 = 7/48.

So, the time it would take the machines to work together is 1/(7/48) = 48/7 = 6 6/7.

Answer: B

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