It's not difficult, 1. When measuring the average speed of 100m for a student, the timekeeper starts to count the time when he hears the starting gun at the end. The result shows that the student's score is 10s. If the speed in the air is 340m / s, what is the actual average speed of 100m 2. There are two rolls of thin copper wire, one of which is marked with the words "(refer to the mark in the figure) = 0.3mm", the other roll of label falls off, and the diameter is unknown. If there is no copper length measuring tool, and you are given two identical pencils, can you measure the diameter of the copper wire more accurately? (refer to the mark in the figure) is a symbol similar to the Chinese character The most important thing is to look at the first question, and the second one is OK without looking at it!

It's not difficult, 1. When measuring the average speed of 100m for a student, the timekeeper starts to count the time when he hears the starting gun at the end. The result shows that the student's score is 10s. If the speed in the air is 340m / s, what is the actual average speed of 100m 2. There are two rolls of thin copper wire, one of which is marked with the words "(refer to the mark in the figure) = 0.3mm", the other roll of label falls off, and the diameter is unknown. If there is no copper length measuring tool, and you are given two identical pencils, can you measure the diameter of the copper wire more accurately? (refer to the mark in the figure) is a symbol similar to the Chinese character The most important thing is to look at the first question, and the second one is OK without looking at it!

The first question is short of 100 / 340 seconds, that is, the total time is 10s + 100 / 340s
The actual average speed of 100 meters is 100 / (10 + 100 / 340) m / s

1.2007 minus 1 / 2 of it, then minus the remaining 1 / 3, finally minus the remaining 1 / 2007, what is the remaining number?
2. At the festival garden party, the first person who enters the park will take one gift and then take the remaining 1 / 10; the second person who enters the park will take two gifts and then take the remaining 1 / 10; the third person who enters the park will take three gifts and then take the remaining 1 / 10; until all the prepared gifts are collected. It turns out that the number of gifts taken by the people who get the gifts is equal, then how many gifts are there? How many people get the gifts?
Note: two questions should be analyzed in detail, according to the specific degree of analysis, I will add 50-200 points!

2007 * (1-1 / 2) * (1-1 / 3) * (1-1 / 4) * '* (1-1 / 2007) = 2007 * 1 / 2 * 2 / 3 * 3 / 4' * 2006 / 2007, the 2 of 1 / 2 is reduced by the 2 of 2 / 3, and the 3 of 1 / 3 is reduced by the 3 of 3 / 4, and so on. If this continues, only 2007 * 1 / 2007 is left, and the result is equal to 1
There are many ways to answer the second question
one
Let the penultimate person take x, then the last person takes x, and there are 0. We can see that the penultimate person takes (x-1) first, and then takes the remaining 1 / 10 (that is, 1 / (10-1) = 1 / 9 of x)
X=(X-1)+1/9X
X-1/9X=X-1
X-8/9X=1
X=9
The total number of gifts is 9 × 9 = 81 (pieces)
two
There are x gifts
1+(X-1)×1/10=2+[(X-1)×(1-1/10)-2]×1/10
X=81
Number of gifts per person: 1 + (81-1) × 1 / 10 = 9
Total number of people: 81 △ 9 = 9 (people)

The two trains, train a and train B, depart from 540 km away from each other at the same time. After 2.5 hours, the two trains meet. It is known that train a travels 96 km per hour on average, and train B travels how many km per hour on average?

What is the speed sum of a and B cars
540 △ 2.5 = 216 (km / h)
Car B runs every hour
216-96 = 120 (km)