5. A and B can do a work in 8 days B and C can do the same work in 12 days. A, B and C together can finished it in 6 days. A and C together can do it in how many days? 1) 4 days 4) 12 days. 2) 6 days 3) 8 days
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5. A and B can do a work in 8 days B and C can do the same work in 12 days. A, B and C together can finished it in 6 days. A and C together can do it in how many days? 1) 4 days 4) 12 days. 2) 6 days 3) 8 days
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Answer:
Let's use the concept of work rates to solve this problem.
Let's denote the work rate of A as "A's rate," the work rate of B as "B's rate," and the work rate of C as "C's rate."
From the information given:
1. A and B together can complete the work in 8 days, so their combined work rate is 1/8 of the work per day: A's rate + B's rate = 1/8.
2. B and C together can complete the work in 12 days, so their combined work rate is 1/12 of the work per day: B's rate + C's rate = 1/12.
3. A, B, and C together can complete the work in 6 days, so their combined work rate is 1/6 of the work per day: A's rate + B's rate + C's rate = 1/6.
Now, let's solve this system of equations to find the individual work rates:
From equation 1, we have:
A's rate + B's rate = 1/8
From equation 2, we have:
B's rate + C's rate = 1/12
From equation 3, we have:
A's rate + B's rate + C's rate = 1/6
Now, let's subtract equation 2 from equation 1 to find A's rate:
(A's rate + B's rate) - (B's rate + C's rate) = (1/8) - (1/12)
This simplifies to:
A's rate - C's rate = (3/24) - (2/24)
A's rate - C's rate = 1/24
Now, we have A's rate - C's rate = 1/24.
We want to find how many days A and C together can finish the work, so we need their combined work rate. Adding A's rate and C's rate:
(A's rate + C's rate) = (A's rate - C's rate) + 2(C's rate) = 1/24 + 2(C's rate)
Now, we know that A, B, and C together can complete the work in 6 days, so their combined work rate is 1/6. Using this information:
A's rate + B's rate + C's rate = 1/6
Now, we can substitute A's rate + C's rate with the expression we found earlier:
(1/24 + 2(C's rate)) = 1/6
Let's solve for C's rate:
2(C's rate) = 1/6 - 1/24
2(C's rate) = 4/24 - 1/24
2(C's rate) = 3/24
C's rate = (3/24) / 2
C's rate = 3/48
C's rate = 1/16
Now, we know C's rate is 1/16. To find out how many days A and C together can finish the work, we can calculate their combined work rate:
A's rate + C's rate = 1/24 + 1/16 = (2/48) + (3/48) = 5/48
Now, we can find the time it takes for A and C together to finish the work by taking the reciprocal of their combined work rate:
Time = 1 / (A's rate + C's rate) = 1 / (5/48) = 48/5 = 9.6 days
So, A and C together can finish the work in approximately 9.6 days.
Since the answer choices are in whole numbers, the closest option is 10 days (rounded from 9.6), which isn't listed among the provided choices.