# Solving the Cistern Filling Problem in 19 Hours

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In summary, the problem is asking how long it will take to fill a cistern if two pipes, one filling in 4 hours and one in 6 hours, are opened alternatively for 1 hour each. After attempting to solve it, the answer is still unclear as the book's answer of 19 hours does not seem possible based on the individual filling times. Further clarification is needed to solve the problem accurately.

## Homework Statement

The problem is as follows
" 2 pipes fill cistern with water in 4 and 6 hours respectively.If the first pipe in 4 and 6 hours
respectively . if the first pipe be opened first and the pipes be opened alternatively one at a time for 1 hour each, in how many hours will the cistern be filled up"
My attempt:
I first took that in 1 hour first pipe fills 1/4th of tank and second pipe 1/6 thof tank
.: in 2 hours they fill 1/4+1/6= 5/12th of tank
in 1hour they fill 5/24 th of tank
.: they fill the tank in 24/5 hours
But the problem is my book's answer is 19 hours.I don't know how that is possible because if they alone fill it in 4 and 6 hours then if they are working together the time should be less.

1/4 + 1/6 is = to 5/12 of the tank filled which is if both of them are filling the tank in one hour so you have to get a further 1/4 and 1/6 of these repectively so 1/4*5/12 and 1/6*5/12 and add them to get the time, maybe you'll get the rite answer...

Hope this helps, confusing problem have to admit.

I am really sorry, but could you please be more precise?

## 1. How does the cistern filling problem relate to science?

The cistern filling problem is a mathematical problem that can be solved using scientific principles and methods. It involves calculating the rate at which water enters and drains from a cistern, which requires an understanding of fluid dynamics and calculus.

## 2. What is the significance of solving the cistern filling problem in 19 hours?

The time frame of 19 hours is significant because it is a relatively short period of time and requires efficient problem-solving skills. Additionally, solving the problem in 19 hours can have practical applications in real-life situations, such as managing water supply in a household or agricultural setting.

## 3. What are the key factors that affect the rate of cistern filling?

The key factors that affect the rate of cistern filling include the size and shape of the cistern, the speed and volume of water entering the cistern, and any obstructions or restrictions in the flow of water. Other factors, such as temperature and atmospheric pressure, can also have an impact.

## 4. How can the cistern filling problem be solved in 19 hours?

The cistern filling problem can be solved by using mathematical equations and principles, such as the rate of change formula and the volume of a cylinder formula. By setting up and solving these equations, it is possible to determine the necessary rate of water flow to fill the cistern in 19 hours.

## 5. What are some real-life applications of the cistern filling problem?

The cistern filling problem has practical applications in many industries, such as agriculture, engineering, and water management. It can also be used to solve problems related to fluid dynamics, such as calculating the flow rate of a river or the filling time of a swimming pool.