Math diary (a strange mathematical roaming) _1 words.

It's crisp in autumn, the air is full of the fragrance of rice flowers, and the river on the mountain is flowing. What a beautiful scene! Dad saw that I was in a good mood, and he smiled. He smiled and approached me and said, "The weather is good, and the thinking is definitely good. Meet the challenge of abstruse mathematics!" Oh, here we go again. Let fate take its course!

When I flip it at will, a question flashes in front of my eyes: A and B water pipes are opened at the same time to fill a pool. After one hour, seven-eighths of the pool can be filled. If A pipe is opened alone for 4 minutes, then B pipe can be opened alone for 3 minutes to fill half of the pool. Please open a water pipe separately. How many hours does it take to fill the pool?

a long time has passed, and I have read the topic again and again. Faced with several scores and time, I just can't start. I was scratching my head and scratching my head, puzzled. I had to beg dad with a bitter face. Dad mysteriously drew the answer from the bookcase, read it for a while, then picked up a red pen and began to speak.

"In the title, the similarity condition is that Party A and Party B are injected with water for 3 minutes both times. The first half-hour * * * water injection amount is 7/8× 1/2 = 7/16, but now we have to start from the second 4 minutes, 4 minutes = 2/3 hours, 1/2-7/16 = 1/16, which is the water injection amount of A alone for 1 minutes. Therefore, 1/16 ÷ (2/3-1/2) = 3/8, which is the efficacy of A, so that the time 1 ÷ 3/8 = 8/3 (hour) can be obtained. The time of B is also easily found to be 1 ÷ 1/2 = 2 hours.

oh, it's so simple! I suddenly realized that I didn't forget to sigh. How many brain cells have I sacrificed to solve a difficult problem! Sorry! Stare at the book, and then take a nap!

brush! Huh? Where am I? I only felt a flash in front of my eyes, and I came to a place like heaven. There are clouds under the feet here, and there is a golden light on an iron gate in front. At this time, an angel-like person, no, just an angel floated by. He said: "The Duke of Zhou deserves to be the Duke of Zhou. He brought a foreign aid so soon!" He talked on the phone, which made me confused.

"Stop it." He dragged me into the gate until I reached a pool. God! The pool again! Just when I recovered, the angel said, "A few days ago, the devil declared war on us, and we couldn't defeat him, so we asked the priest for help. We had to work out this question, and if we couldn't answer it, we would go to war ..."

"This pool has a volume of 1 cubic meters, and it has two water inlet pipes A and B and a drainage pipe. Both pipes A and B enter the water at the same time and the drainage pipe discharges water, which takes 6 hours to finish the water discharge; It takes 1 hours and 15 hours for A and B pipes to fill the pool separately. If A pipe enters water and the drain pipe drains water, it takes 2 hours to drain the water in the pool. So how many cubic meters of water was there in the pool? "

I was elated and thought, Now you've hit the muzzle! After a little thinking, I brewed for a while, and I said with my mouth open: "The 6-hour water injection volume of the two pipes A and B is (1/1+1/15) × 6 = 1, which shows that the 6-hour water injection volume of the drainage pipe is 1 cubic meters+the original water volume, and there is some water in the pool. If A and the drainage pipe are opened together for 2 hours, the water discharge volume is 1× 1/5 cubic meters+the original water volume. Therefore, the 6-2=4-hour discharge of the drainage pipe is 1× (1-1/5) = 8 cubic meters, and the hourly discharge of the drainage pipe is 8÷4=2 cubic meters. Therefore, there is water in the original pool: 2×6-1=2 cubic meters.

the angel looked at me blankly, and it took a long time to react. Just woke up and hugged me and shouted, "God, this is really a genius!" " I laughed when I heard it, and it felt good to be praised! Hehehehehehe ...

"What are you giggling about!" Dad's cry suddenly sounded in his ear. I couldn't help shivering. Open your eyes and see, it's still the same table, the same draft. It turned out to be a fugue! What a strange mathematical roaming! Hehe hehe ...