Question

It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled. How long would each pipe take to fill the swimming pool.

Answer 1

Answer:

40 hrs

Step-by-step explanation:

It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled. How long would each pipe take to fill the swimming pool.

Let A and B be two pipes.

So in 1 hour quantity of water filled by pipe A is 1/A and that of pipe B is 1/B. The quantity of water filled by both pipes in one hour is 1/A + 1/B

It takes 24 hours by pipes to fill the pool

So 1/A + 1/B = 1/24------------(1)

The quantity of water filled in 8 hours by pipe A = 8/A

The quantity of water filled in 18 hours by pipe B = 18/B

Given in the question half is filled so

8/A + 18/B = 1/2-------------(2)

From (1) and (2) we have,

x + y = 1/24-------------(3)

8 x + 18 y = 1/2----------(4)

Multiply eqn (3) by 8 and eqn (4) by 1

8 x + 8 y = 1/3

8 x + 18 y = 1/2

Subtracting we get

- 10 y = - 1/6

y = 1/60

So we have B = 60

The second pipe alone fills in 60 hours

Substituting y = 1/60 in eqn (3) ,

x + 1/60 = 1/24

120 x = 3  

x = 3/120 = 1/40

So A = 40 hours

So it will take 40 hours , if the first pipe alone fills the pool.

Answer 2

Answer:

There are many ways to set up the problem to be solved algebraically; and there are many different ways to solve the system of equations that leads to the answers.

The following is one path to the solution; perhaps other tutors will show very different paths.

Let x be the fraction of the pool filled in 1 hour by the larger pipe and y be the fraction filled in 1 hour by the smaller pipe. Then

24x%2B24y+=+1 [the two pipes together for 24 hours fill the whole pool]; and

8x%2B18y+=+1%2F2 [the larger pipe for 8 hours, plus the smaller pipe for 18 hours, fills 1/2 of the pool]

With the two equations in this form I would solve the system by elimination. Multiplying the second equation by 3 gives us

24x%2B54y+=+3%2F2

Then comparing it to the first equation (that is, subtracting one equation from the other) gives

30y+=+1%2F2

y+=+1%2F60

So the smaller pipe fills 1/60 of the pool in 1 hour, which means it takes 60 hours to fill the pool by itself.

Then substitute this value for y in either of the original equation to solve for x:

24x%2B24%2F60+=+1

24x%2B2%2F5+=+5%2F5

24x+=+3%2F5

x+=+3%2F120+=+1%2F40