There are many simple methods to solve mathematical operations, such as mathematical formula operation, rounding calculation, benchmark number method, common factor extraction method and so on. According to the questions frequently tested, some special questions, such as age, tree planting, travel and so on. It is also summarized. Each type of problem also has different solutions, and we will explain them to you one by one. Today, I mainly talk about the solutions to engineering problems.
The quantitative relationship of some fractional problems is the same as that of "total workload, work efficiency and work time" in integer application problems, but the total workload is not directly given in the stem of the problems. Practical problems like this are usually called engineering problems.
The basic quantitative relationship of engineering problems is:
Total workload = sum of each workload
Workload = working efficiency × working hours
Efficiency = workload/working hours
Working hours = workload/work efficiency
Collaborative work efficiency = collaborative workload/collaborative work time
Engineering problems are not only road construction, building houses and transporting goods, but also problems, such as water injection in pools. Find out the key points of workload, work efficiency and work time loss in engineering calculation problems.
To analyze and solve engineering problems, first of all, according to the characteristics of the topic, the total workload is expressed as "1", and the work efficiency can be expressed as "a fraction" of the total workload that can be completed in unit time. The total workload referred to here can be both the total workload and part of the workload; The work efficiency mentioned here can be obtained not only by working hours, but also by the progress and change law of the "project". In short, it must be decided through specific actual conditions.
Let's look at a few examples to help you get familiar with the idea of solving engineering problems:
Example 1 Party A, Party B and Party C jointly build a road. It took Party A and Party B five days to repair the 1/3 road, Party B and Party C two days to repair the remaining 1/4 road and five days to repair the remaining roads. Q: How many days does it take B to build a road by himself?
A.24 B.40 C.32 D.60
Answer and analysis A. Let the road project be 1,
The efficiency of cooperation between Party A and Party B is:1/3÷ 5 =115;
The efficiency of cooperation between Party B and Party C is: (1-1/3) ×1/4 ÷ 2 =112;
The cooperation efficiency of Party A and Party C is [1-1/3-(1-kloc-0//3) ×1/4] ÷ 5 =1/kloc-0.
Therefore, the efficiency of tripartite cooperation among Party A, Party B and Party C is: (115+112+110) ÷ =1.
So the work efficiency of B is1/8 ――110 =1/40;
So it costs 40 yuan for B to build a road alone.
Example 2 Two people, Party A and Party B, carried the goods together, which was originally planned to be completed in 10 hour. However, in the process of handling, Party A has to work six hours less. As a result, it took them 14 hours from start to finish. Find the efficiency of b ().
1/24 b . 1/25 c . 1/30d . 1/60
Answers and analysis C.
(1) can do equations, but it is a waste of time. If the working efficiency of A is X, then B is110-x,14× (110-x)+(14-x).
(2) If Party A doesn't delay and two people work together for 14 hours, the task will be overfulfilled, which is exactly what Party A didn't do for 6 hours, so the work efficiency of Party A is: (110×14-1) ÷. You should choose C.
The production team expects to finish repairing a canal within 30 days. I. Project of 18 people 12 days repair13. If the project is to be completed six days ahead of schedule, how many more people will be added? ( )
A. 18
Answer and analyze a.
(1) 18 people 12 days to complete the project, with 2/3 remaining and 12 days remaining. If the project is doubled, the number of people can only be doubled, that is, 18 people will be increased. Choose a.
(2) A person's working day is called "working day". According to "18 people 1/3 days to complete the project", it takes 18× 12 = 2 16 working days to complete the project, and the remaining working days are: 265438+. The remaining days are: 30- 12-6= 12 days; The number of people needed for the remaining work is: 432 ÷12 = 36; The number of people to be increased is: 36- 18= 18, so the correct answer is a.
Through the above examples, we understand the basic characteristics of engineering problems and some solutions to engineering problems.
In fact, the test point of mathematical operation is not the knowledge accumulation of candidates, but the reaction speed and adaptability of candidates. Therefore, the topic of mathematical operation does not require candidates to use complex mathematical formulas to operate (although the results can be calculated in the end), but requires candidates to skillfully use simple methods to answer according to the conditions given in the topic. Today, I introduced the method of solving engineering problems, which is also a common problem in mathematical operation. I hope you can grasp the main points and use them flexibly. Other problem-solving methods will be introduced one by one in the future. I suggest that while learning problem-solving methods, we should also pay attention to the accumulation of basic knowledge, do more exercises and apply all kinds of problem-solving methods to the extreme.