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9. Three people A, B, and C are working in a factory. A and B working together can finish a task in 18 days whereas B and C working together can do the same task in 24 days and A and C working together can do it in 36 days. In how many days will A, B, and C finish the task working together ?*16201525

Question

9. Three people A, B, and C are working in a factory. A and B working together can finish a task in 18 days whereas B and C working together can do the same task in 24 days and A and C working together can do it in 36 days. In how many days will A, B, and C finish the task working together ?*16201525

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Solution 1

To solve this problem, we first need to find the rates at which A, B, and C work.

  1. A and B can finish the task in 18 days, so their combined rate is 1/18 tasks per day.
  2. B and C can finish the task in 24 days, so their combined rate is 1/24 tasks per day.
  3. A and C can finish the task in 36 days, so their combined rate is 1/36 tasks per day.

If we add these three rates together, we get (1/18 + 1/24 + 1/36) = 1/9 + 1/12 + 1/18 = 4/36 + 3/36 + 2/36 = 9/36 = 1/4 tasks per day.

However, this is the rate for two people working together, and we have counted the rate for each person twice. So, the rate for all three people working together is half of this, or 1/4 / 2 = 1/8 tasks per day.

Therefore, A, B, and C working together can finish the task in 8 days.

This problem has been solved

Solution 2

To solve this problem, we first need to find the rates at which A, B, and C work.

  1. A and B together can finish the task in 18 days. So, their combined rate is 1/18 tasks per day.
  2. B and C together can finish the task in 24 days. So, their combined rate is 1/24 tasks per day.
  3. A and C together can finish the task in 36 days. So, their combined rate is 1/36 tasks per day.

If we add these three rates together, we get the sum of two times the rates of A, B, and C.

So, 2*(A's rate + B's rate + C's rate) = 1/18 + 1/24 + 1/36.

To simplify this, we need to find a common denominator for 18, 24, and 36. The least common multiple of these numbers is 72.

So, 2*(A's rate + B's rate + C's rate) = 4/72 + 3/72 + 2/72 = 9/72.

Dividing both sides by 2, we get A's rate + B's rate + C's rate = 9/144 tasks per day.

So, A, B, and C together can finish the task in 144/9 = 16 days.

This problem has been solved

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