SOLUTION: If it takes 24hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of smaller diameter is used for 18 hours, only half of

Algebra ->  Linear-equations -> SOLUTION: If it takes 24hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of smaller diameter is used for 18 hours, only half of       Log On


   

Question 1132877: If it takes 24hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of 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 by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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

So the larger pipe fills 1/40 of the pool in 1 hour, which means it takes 40 hours to fill the pool by itself.