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

Number 40 is a rational number glad i could