Example 1 A project, team A needs 12 days, team B needs 20 days, and how many days does it take for two teams to work together?

Analysis shows that the total amount of this project is "1". Team A completes the project in one day112; Team B completed1/20 of the project in one day; (112+1/20) = 2/ 15, how many 2/15 are included in the total work "1",that is, two teams complete the project together.

1÷ (112+1/20) = 7.5 (days)

This is the basic problem of an engineering problem. Take the total workload as the unit "1", divide the total workload by the sum of work efficiency, and you can find out the time taken to complete the project.

Second, answer with the number of copies.

For a project, it takes 12 days for Party A to do it alone and 15 days for Party B to do it alone. Now Party A has worked alone for three days, how many days will it take for Party B to join?

According to the analysis, the total amount of this project is divided into (12× 15) shares on average, and it takes 12 and 15 days for Party A and Party B to complete this project respectively. It is known that Party A and Party B can complete 15 and 12 shares respectively every day, which can be completed jointly (. That is, (15×3) copies have been made, and the rest are (12×15-15× 3) copies. The time required for joint production after Party B joins is (12× 15-65438).

When commenting on this kind of application problems, the key is to regard the product of the time required for A and B to do it alone as the total number of copies.

Third, use multiple relationships to solve.

It took 65,438+04 days for the master to process a batch of parts. If the master and the apprentice work together for 10 days, how many days does it take for the apprentice to work alone?

Analysts do 10 days+apprentices do 10 days to complete all the work;

The master finished all the work in 14 days (10 days +4 days); It can be seen that the master's workload of 4 days = the apprentice's workload of 10, that is, the master's work efficiency is 2.5 times that of the apprentice, so the apprentice 14×2.5=35 (days) is needed to complete it alone.

When solving this problem, the master's work efficiency is 2.5 times that of the apprentice, so we can simply find out the number of days that the apprentice needs to do this alone.

The above-mentioned cases, due to the adoption of some special methods for analysis and thinking, can turn the difficult into the easy, simplify the complex, provide a new method for solving engineering problems, open up students' problem-solving ideas and cultivate their creative thinking ability.