It takes pipe A 14 days to fill the fish pond. It takes pipe B 18 days to fill the same pond. Find out how pond it takes both pipes working together to fill the pond

A's rate = 1/14

B's rate = 1/18
combined rate = 1/14+ 1/18 = 8/63

time at combined rate = 1/(8/63) = 63/8 or 7 days , 21 hours

To find out how long it takes for both pipes A and B to fill the pond when working together, we can use the concept of rates.

First, we determine the rates at which each pipe fills the pond. The rate at which pipe A fills the pond is 1/14 pond per day, as it takes 14 days to fill the pond completely. Similarly, the rate at which pipe B fills the pond is 1/18 pond per day since it takes 18 days to fill the pond.

To find the combined rate when both pipes are working together, we add the individual rates. So, the combined rate is 1/14 + 1/18 pond per day.

To add these fractions, we need a common denominator. The least common multiple of 14 and 18 is 126. Multiplying the fractions by the appropriate factors to achieve a common denominator, we get (9/126) + (7/126) pond per day, which equals 16/126 pond per day.

Now, we can express the combined rate as a single fraction: 16/126 pond per day.

To find out how long it takes both pipes working together to fill the pond, we divide 1 (representing the whole pond) by the combined rate:

1 pond รท (16/126 pond per day) = 126/16 days.

Simplifying this fraction, we get 7.875 days.

Therefore, it takes both pipes A and B approximately 7.875 days to fill the pond together.