1.A and b water pipes need 20 hours and 16 hours to open and fill a pool of water respectively. It takes 10 hour to open the water pipe C alone to drain a pool of water. If there is no water in the pool, open water pipes A and B at the same time. After 5 hours, open the drain pipe C again. How many hours does it take to fill the swimming pool?

Solution:1/20+116 = 9/80 indicates the working efficiency of both parties; 9/80× 5 = 45/80 indicates the water inflow after 5 hours; 1-45/80 = 35/80 indicates the required water inflow; 35/80 ÷ (9/80-110) = 35 means it takes 35 hours to fill it; A: It will take 35 hours to fill the pool after 5 hours.

It takes 20 days for Team A and 30 days for Team B to build a canal. If two teams cooperate, the work efficiency will be reduced because of the influence of each other's construction. The working efficiency of team A is four fifths of the original, while that of team B is only nine tenths of the original. Now it is planned to complete the canal in 16 days, and it is required that the two teams cooperate for as few days as possible. So how many days will the two teams cooperate?

Solution: From the meaning of the question, the work efficiency of Party A is 1/20, that of Party B is 1/30, and that of both parties is1/20 * 4/5+1/30 * 9//kloc-0. A's work efficiency >: B's ergonomics. Because it is required that "the fewer days the two teams work together, the better", Party A should be made to work faster./kloc-If it is too late within 0/6 days, Party A should cooperate with Party B..

Only in this way can the two teams work together as little as possible. If the cooperation time is X days, then the time for Party A to do it alone is (16-x) days; 1/20 *( 16-x)+7/ 100 * x = 1； X = 10 A: The shortest cooperation time between Party A and Party B is 10 days.

The benefits of learning mathematics

People who are good at math are relatively smart and savvy, and they can show their advantages in dealing with people. The faster you think, the more ways and ideas you have. Cambridge, majoring in financial mathematics at Carnegie Mellon University in the United States, said that studying mathematics has brought her mental exercise and made me pay more attention to the rigor of thinking in my life.

Can manage money better than others. The application of mathematics in life is everywhere. Nowadays, the society is already an information society, and mathematical knowledge is used in financial management and computers. Warren Buffett is very powerful, but Buffett's power is also based on mathematics. Buffett's decision-making process is actually the method of using subjective probability.