it can take 12 hours to fill a swimming pool using two pipes. if the larger pipe is used for 4hrs and the smailler pipe of 9 hr only half the pool can be filled. how long will take each pipe to fill the pool seperately

large pipe = 20 hours

small pipe = 30 hours

x = larger pipe

y = smaller pipe

12 hours to fill swimming pool with both pipes:

12x + 12y = 100%

4 hrs large pipe and 9 hrs small pipe fills half the pool:

4x + 9y = 50

4x = 50 - 9y

substitute "4x" in first equation with "50 - 9y" to solve for y:

12x + 12y = 100

3 (4x) + 12y = 100

3 (50 - 9y) + 12y = 100

150 - 27y + 12y = 100

150 - 15y = 100

-15y = - 50

y = 50/15 = 10/3 = 3 1/3

every hour, the small pipe fills the pool 3 1/3%

Now use the value for y to solve for x:

12x + 12y = 100

12x + 12 (10/3) = 100

12x + 40 = 100

12x = 60

x = 5

every hour, the large pipe fills the pool 5%

if the large pipe were filling the pool by itself, t = time it takes to fill 100%:

100% = t * 5

20 = t

It would take 20 hours for the larger pipe to fill the pool by itself

for the smaller pipe:

100% = t * 10/3

300/10 = t

30 = t

it would take 30 hours for the smaller pipe to fill the pool by itself