3 pipes are used to fill apool with water .Individually they can fill that pool in 9hr ,6hr ,3hr .how many minutes will it take to fill the pool if all 3 pipes are used simultaneously?
The individual rates are A=1/3, B=1/6 and C=1/9 pools per hour.
Their combined rate derives from
T = ABC/(AB + AC + BC).
Another version of this type of problem should show you its derivation.
It takes Al 5 hours to paint a shed, Ben 10 hours and Charlie 15 hours. How long would it take all three to paint the shed working together?
1--A can paint the shed in 5 hours.
2--B can paint the shed in 10 hours.
3--C can paint the shed in 15 hours.
4--A's rate of painting is 1 shed per A hours (5 hours) or 1/A (1/5) shed/hour.
5--B's rate of painting is 1 shed per B hours (10 hours) or 1/B (1/10) shed/hour.
6--C's rate of painting is 1 shed per C hours (15 hours) or 1/C (1/15 shed/hour.
7--Their combined rate of painting is therefore 1/A + 1/B + 1/C = (AC + BC + AB)/ABC = (1/5 + 1/10 + 1/15) = (11/30 sheds /hour.
8--Therefore, the time required for all of them to paint the 1 shed working together is 1 shed/(AC+BC+AB)/ABC sheds/hour = ABC/(AC+BC+AB) = 5(10)15/[5(15)+10(15)+5(10) = 30/11 hours = 2.7272 hours = 2hr-43min-38.18sec.
Note - The time required to complete a single "specific task" by three individuals working together, who can complete the task individually in A, B, and C units of time is ABC/(AC + BC + AB).
To find out how many minutes it will take to fill the pool if all three pipes are used simultaneously, we need to calculate the combined filling rate of the pipes.
Let's denote the filling rates of the three pipes as follows:
- Pipe A: 1 pool per 9 hours
- Pipe B: 1 pool per 6 hours
- Pipe C: 1 pool per 3 hours
To calculate the combined filling rate, we need to find the sum of the individual filling rates. Therefore, the combined filling rate is:
1/9 + 1/6 + 1/3
To add these fractions, we need to find a common denominator, which in this case is 18. The combined filling rate becomes:
(2/18) + (3/18) + (6/18) = 11/18 pools per hour
Since there are 60 minutes in an hour, we can convert the filling rate to minutes by dividing it by 60:
(11/18) x (1/60) = 11/1080 pools per minute
Therefore, it will take approximately (1080/11) minutes to fill the pool if all three pipes are used simultaneously, which is approximately 98.18 minutes.