Solution: We open the water inlet pipe 1 hour, then open the water outlet pipe 1 hour, and then close the water outlet pipe. The water inlet pipe and the water outlet pipe open and close a cycle in this order. The key to this problem is to determine how many cycles it takes to open the water inlet pipe and fill it with water. We assume that the water inlet pipe can be opened for y hours after at least x cycles, so the time for filling the pool with water is 2x+y. According to the meaning of the question, we can draw the following conclusions:

( 1/5- 1/8)x+ 1/5 & gt； 1 ……………………①

4/5 & lt； ( 1/5- 1/8)(x- 1)+ 1/5 & lt； 1 …………②

( 1/5- 1/8)x+y = 1……③

Solve the inequality group consisting of ① and ②, and get

10 2/3 & lt； x & lt 1 1 2/3

According to the meaning, x can only be an integer, so

x= 1 1

Substitute 3 to get

( 1/5- 1/8)* 1 1+y = 1

solve

y=7/8

Therefore, the time when the pool is filled with water is:

2x+y = 2 * 1 1+7/8 = 22 7/8

A: It takes at least 22 7/8 hours to fill the swimming pool.