tap A takes 60 minutes to fill a bucket tap B takes 30 minutes and tap C take 15 minutes. how much time it will take to fill a bucket if opened all 3 at once

1/T = 1/60 + 1/30 + 1/15 = 7/60

9.25

To calculate the time it will take to fill a bucket when all three taps (A, B, C) are opened at once, we need to determine the rate of fill for each tap.

First, let's calculate the rate of fill for each tap. The rate is measured in "buckets per minute."

- Tap A takes 60 minutes to fill a bucket, so its rate of fill is 1/60 of a bucket per minute.
- Tap B takes 30 minutes to fill a bucket, so its rate of fill is 1/30 of a bucket per minute.
- Tap C takes 15 minutes to fill a bucket, so its rate of fill is 1/15 of a bucket per minute.

Now, let's add up the rates of fill for all three taps:
Rate of fill = Rate of Tap A + Rate of Tap B + Rate of Tap C

Rate of fill = 1/60 + 1/30 + 1/15
Rate of fill = (2/120) + (4/120) + (8/120)
Rate of fill = 14/120

Therefore, when all three taps are opened at once, the combined rate of fill is 14/120 of a bucket per minute.

To determine the time it will take to fill a bucket, we take the reciprocal of the rate of fill:
Time to fill a bucket = 1 / Rate of fill
Time to fill a bucket = 1 / (14/120)
Time to fill a bucket = 120 / 14
Time to fill a bucket ≈ 8.57 minutes

So, it will take approximately 8.57 minutes to fill a bucket if all three taps (A, B, and C) are opened at once.