After analyzing and summarizing a large number of elevator test questions, the national civil service network civil service examination counseling experts believe that after mastering the basic formula, the elevator test questions can get the correct answer in a short time with very simple algebraic method or equation method. Taking two test questions as examples, this paper introduces a simple algorithm for solving elevator test questions.
Example 1: The escalator in the shopping mall runs at a constant speed from bottom to top. Two children walk up and down the escalator. The girl walks up from the bottom and the boy walks down from the top. As a result, the girl walked 40 steps upstairs and the boy walked 80 steps downstairs. If a boy takes twice as many escalator steps per unit time as a girl, when the escalator is stationary, the visible escalator steps are (). In 2005, the national civil service examination, the administrative professional ability test, was really a second-class volume-47 questions
A.40 level B.50 level C.60 level D.70 level
According to the meaning of the question, the boy walked by the elevator and the elevator helped the boy. The boy took 80 steps more than the escalator when the elevator was stationary. The boy took some wrong paths because the elevator helped him. On the other hand, girls walk along the elevator, which helps girls move forward. In other words, girls walk 40 steps less than when they are at rest, and with the help of the elevator, girls walk fewer steps. Obviously, the distance ratio between boys and girls is 80: 40 = 2: 1, and according to the meaning of the question, the number of escalator steps taken by boys per unit time is twice that of girls, which means that the speed of boys is twice that of girls. So far, we can know that the distance ratio of boys and girls is equal to the speed ratio, which means that the time for boys and girls to climb the escalator is equal, which means that the time for the escalator to help boys and girls is equal. Moreover, because the speed of the escalator is certain, we can introduce the escalator, so that boys walk more distances than static escalators, and girls walk less distances than static escalators, and the distance between them is equal. So we just need to say that the sum of the distances that boys and girls walk offsets that boys walk twice as much as girls. So the answer to this question is
(80+40)÷2=60 。 The thinking process of this problem is clear and clear. If candidates want to solve problems more intuitively, they can also draw pictures, and the specific process can be demonstrated by themselves.
Although the above process seems complicated, in fact, the thinking process can be completed in a few seconds. I hope candidates can master the problem-solving skills of this kind of questions as soon as possible.
The above explains a simple solution to the elevator test questions in the national civil service examination. Next, let's look at a question that was strategically abandoned by most candidates in the exam, but it is not difficult to do.
Example 2: A and B walk from bottom to top on the escalator rising at a constant speed, and A takes twice as many steps per minute as B; When A goes to the top at level 36 and B goes to the top at level 24. So, how many steps of the escalator are exposed? () 2007 Shandong Province Civil Servant Examination Administrative Professional Ability Test Zhenti -55 questions
A. 68 BC to 56 BC
If we solve this problem by solving equations, it will take candidates at least three minutes, which is obviously a very unwise choice in the exam.
Many candidates give up this question from a strategic point of view because there is no way to answer it. In fact, if the method is correct, candidates can get the correct answer in a short time. Next, we use equation solving and algebraic operation to solve this problem.
Method 1: Equation method
If we set up an escalator with n floors exposed, we can list the following equation:
, get N=72.
On the left side of the equation, the numerator is the number of steps that A helps A walk, and the denominator is the number of steps that B helps B walk. Because the speed of the escalator is constant, the distance ratio is equal to the time ratio, that is, the time ratio for A and B to help A and B reach the top respectively, and because A and B are synchronized with the elevator, this ratio is also the time ratio for A and B to reach the top. In these two modes, A takes 36 escalators and B takes 24 escalators. Since the number of escalators A takes per minute is twice that of B, that is to say, the speed ratio of A and B is 2: 1, the right side of the equation is the time ratio of A and B to the top, so the above equation can be listed and the result can be obtained.
Method 2: Algebraic method
The above is the thinking process and solving process of solving this problem by equation method, and then we introduce a more concise algebraic method.
According to the meaning of the question, we know that the speed ratio between Party A and Party B is 2: 1, so when Party A reaches the top of the escalator, that is, Party A takes 36 steps, and Party B takes 18 steps. Because the speed of the elevator they take is the same and synchronous, the distance traveled by the elevator in both directions is the same. At this time, Party B is still 36- 18 steps away from the summit. And B has taken 24 steps to the top, and has already taken 18 steps, and still needs to take 24- 18=6 steps, and there are still 18 steps from the top, which means there are still 18-6= 12 steps to take the escalator. From this, we can infer that the speed ratio between the escalator and B is 12: 6 = 2: 1. Because the distance ratio is equal to the speed ratio at the same time, that is to say, the speed of the escalator is equal to that of A, so the distance between A and the escalator at the same time is equal, so the number of escalators is 36×2=72. The above two methods are very simple, and it is recommended for you to use them.
To sum up, the elevator question is indeed a kind of difficult problem in the travel problem, but it is also a kind of technical problem in the travel problem, so I suggest that you don't just list equations, let alone rely on "guessing", but think about the problem from the most basic formula, and the original intention of the proposer is to hope that you can answer such questions with simple algorithms, which is also the charm of the travel question.