When answering questions about the relationship between the number of tests, the special value method will appear in my mind from time to time. "Can I set a 100 question to make the method simpler?" Application of special value method in it.
Method 1: When multiple working hours for completing a job are known, let the total work amount be the least common multiple of the working time.
Example 1. Four engineering teams A, B, C, and D build a road. A and B cooperation can be completed in 8 days, and A, C, or B and D cooperation can be completed in 7 days. Asking C and D cooperation can be better than A and B. How many days before the cooperation is completed?
Method 2: When the working efficiency ratio is known, set the ratio to the working efficiency.
Example 2. The work done by A in one day is equal to the work done in B for two days, and the work done in C for 3 days. The existing project can be completed in 2 days. Q How long does it take for B and C to work together?
A. 12 days B. 5 days C. 2.4 days D. 10 days
[Answer] C. Analysis by the public: From the question, we can know that the working efficiency ratio of A, B, and C is 6: 3: 2, and the working efficiency of A, B, and C can be set to 6, 3, and 2, respectively, so the total work is 6 × 2 ﹦ 12. It takes 12 ÷ (3 + 2) ﹦ 2.4 days for B and C to cooperate. Choose option C.
Method three: When multi-labor cooperation, set the workload per person or item per unit time to 1.
Example 3. To build a highway, assuming that everyone has the same daily work efficiency, 180 workers are planned to be completed in 1 year. After 4 months of work, due to special circumstances, it is required to complete the task 2 months in advance. How many workers do you need to add?
A.50 B.65 C.70 D.60
[Answer] D. Zhong Gong analysis: If the workload of each person is 1 for a month, the total workload is 180 × 12, 4 months have been worked, and the remaining workload is 180 × (12-4) ﹦ 180 × 8, which requires 2 months in advance When finished, there are only 6 months left to work, and the amount of work to be completed each month is 180 × 8 ÷ 6 ﹦ 240, which means 240 workers, so it is necessary to increase 240-180 ﹦ 60, and choose option D.
Through the above three questions, I believe that the students have a corresponding understanding of using special value method to solve engineering problems. Through follow-up exercises, Zhong Gong Education believes that everyone can learn from these questions.
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