Please help me answer the question-

Question

It can take 12 hours to fill a swimming pool using two pipes. If the pipe of the larger diameter is used for 4 hours and that with the smaller diameter is used for 9 hours only half the pool is filled. How long will it take or each pipe to fill the pool separately.

Answer 1

1/L + 1/S = 1/12

consider what happens in 1 hour

the Larger fills 1/20, the Smaller fills 1/30, together they fill 1/12

1/20 + 1/30 + 1/12

multiply by 120

120/20 + 120/30 + 120/12

6 + 4 = 10

the Larger fills the pool alone in 20 hours, the Smaller fills the pool alone in 30 hours

together they fill it in 12 hours

in 4 hours for the Larger and 9 hours for the Smaller they fill half in 9 hours

multiply by 2

in 8 hours for the Larger and 18 hours for the Smaller, they fill it in 18 hours

12 hours & 12 hours each fill it all

8 hours for L and 18 hours for S fill it all

4 hours for L is equivalent to 6 hours for S

12 and 12 fill it all

8 and 18 fill it all

4 and 24 fill it all

0 L and 30 S fill it all

or

16 and 6 fill it all

20 L and 0 S fill it all