It takes 12 hrs to fill a swimming pool using two pipes. If the pipe of the larger diameter is used for 4 hrs and the pipe of smaller diameter for 9 hrs, only half the pool can be filled. How long would it take for the pipe with larger diameter to fill the pool?

Given:

Two pipes: 12 hrs (full pool)

Large 4 hrs + Small 9 hrs: 1/2 pool

Calculations:

Half pool filled by both in 6 hrs (12/2)

Let half pool be 1 unit of work.

4L + 9S = 1 (half pool)

L + S = 1/6 (half pool)

L = 1/6 - S

4(1/6 - S) + 9S = 1

2/3 - 4S + 9S = 1

5S = 1/3

S = 1/15 (small pipe for half pool)

L = 1/6 - 1/15 = 3/30 = 1/10 (large pipe for half pool)

Large pipe to fill half pool: 1 / (1/10) = 10 hrs

Large pipe to fill full pool: 10 × 2 = 20 hrs

∴ Large pipe: 20 hrs