If A and B together can complete a work in 18 days. A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-
Let's denote the work done by A in one day as "a," the work done by B in one day as "b," and the work done by C in one day as "c."
We are given the following information:
- A and B together can complete a work in 18 days, so their combined work rate is 1/18 per day.
- A and C together can complete a work in 12 days, so their combined work rate is 1/12 per day.
- B and C together can complete a work in 9 days, so their combined work rate is 1/9 per day.
Now, we can set up a system of equations based on these work rates:
- a + b = 1/18
- a + c = 1/12
- b + c = 1/9
We need to find the work rate of B alone, which is "b." To do that, we can subtract equation (2) from equation (1):
(a + b) - (a + c) = (1/18) - (1/12) b - c = (1/18) - (1/12)
Now, we can solve for "b":
b = (1/18) - (1/12) + c b = (2/36) - (3/36) + c b = (-1/36) + c
Now, we'll use equation (3) to express "c" in terms of "b":
b + c = 1/9 c = (1/9) - b
Substitute this expression for "c" back into the equation for "b":
b = (-1/36) + [(1/9) - b]
Now, solve for "b":
b + b = (-1/36) + (1/9) 2b = (-1/36) + (4/36) 2b = 3/36 b = (3/36) / 2 b = 1/24
So, B alone can do the work in 24 days.
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