In daily life, do a job, make a product, complete a project, etc. , all involve the total amount of work, working time (the time required to complete the total amount of work) and work efficiency (the amount of work completed in a unit time). Exploring the relationship between these three quantities is called "engineering problem".
Engineering problem is the focus of mathematics application problem teaching in primary and secondary schools, the extension and supplement of fractional application problem, and an important tool to cultivate students' logical thinking ability.
The skills of solving engineering problems in primary schools are as follows:
Formula: The total project amount is set to 1, and 1 divided by time is the work efficiency. When a person does it, the work efficiency is his own. You do it once, and the work efficiency is the sum of everyone's efficiency. 1 Subtract what you did not do, and divide what you did not do by the work efficiency, and it is the result.
Example: A project will be completed in 4 days by yourself and 6 days by yourself. Party A and Party B will do it for 2 days at the same time, and then Party B will do it alone. How many days will it take? [1-(1/6+1/4) x2]/(1/6) =1(days).
1. In engineering problems, there are generally three quantities: total workload, working time, that is, the time required to complete the total workload, and work efficiency, that is, the workload completed in unit time;
2. There are the following relationships among these three quantities: working efficiency times working time equals total work, total work divided by working time equals working efficiency, and total work divided by working efficiency equals working time;
3. Special value method: starting from working hours, set the total amount of work as the least common multiple of time. Starting with work efficiency, first find the simplest efficiency ratio, and then determine the value of the total work;
4. Use positive-negative ratio: when working hours are fixed, the total workload is equal to the direct ratio of working efficiency, when working efficiency is fixed, the total workload is equal to the direct ratio of working hours, and when the total workload is fixed, the working efficiency is equal to the inverse ratio of working hours.