Mathematical panic island 3

I did it. I've been thinking for a long time! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 1, fill in the blanks

The two trains are 102m long, 20m seconds, 120m long and 17m/ s respectively. How many seconds does it take for two cars to chase the first train and the second train in the bank?

2。 Someone got off the train from behind and walked at a speed of 2 meters per second, which was longer than him 10 second. After training for 90 meters, he found the speed of the train.

3。 The two existing trains are in the same direction at the same time. The express train exceeds the local train 18 meters per second. 12 seconds later, the mountain climbs at a speed of 10 meter per second. If two trains are on the same road at the same time, after 9 seconds, both trains are climbing the slope, and the length of the two trains is found.

It takes 30 seconds for a train to pass through a tunnel of 3 10 meters and a bridge of 40 meters at the same speed. What is the running speed and body length of the train?

Xiaoying and Mandy of 5 measured the running speed and body length of the zipper in the train. They spent two stopwatches. Xiaoying noticed that the train took 15 seconds from her; Xiaomin is on a table. It takes 20 seconds for two telephone poles to write from the front to the first wire at the back. The distance between two telephone poles is 100 meter. Can you help calculate the length and speed of the train?

It takes 40 seconds for a train to cross a 530-meter-long bridge, and 30 seconds for a 380-meter-long train to cross a cave at the same speed. Find out how many meters the train speed and body length are.

7。 Following the clues of the railway line, starting from two places, at the same speed, the whole train leaves from one side for more than 10 seconds, 130 B meets the train. After the whole train left B 9 seconds, how long did it take for them to meet?

This problem is the catch-up problem of the "train". The "catch" here means that the second train catches up with the last head of the first train, and the "left" is the line drawn by the second train before the first train arrives. The picture is as follows:

It takes x seconds for a group to catch up with two trains from the first train and leave the second train. The equation is:

102+ 120+ 17 = 20.

X = 74 .

2。 The painting part is as follows:

head

90 meters

10 times

/& gt； The train speed is x meters per second, and the equation is listed.

10 X = 90 +2× 10

X = 1 1

& lt bromine

Tail/head

express

head

/& gt； Slow tail

head

quick

head

Tail BR/& gt；; Not used

3。 (1) In front of Qi, draw the following lines while driving in the same direction:

Fast length:18×12-10×12 = 96 (m)

(2) Later, Sarkozy drew the following line chart at the same time and in the same driving direction:

Boss .../> tail

express

head

climb mountains

head

quick

head

finally

slow

Climbing length:18× 9-10× 9 = 72m.

4。 (1) Train speed: (440-310) ÷ (40-30) =13 (m/s).

(2) Body length: 13×30-3 10 = 80 (m)/a >

5( 1) The train speed is:100 ÷ (20-15) × 60× 60 = 72,000 (m/h).

(2) Body length: 20×15 = 300m.

The train body length is x meters and the fuselage length is y meters.

①②

solution

& gt Let the train body be x meters long, A, B and two Y meters per second, and the train line be z meters per second. List the equations according to the meaning of the question.

①②

①-② is also true.

What time does the train leave b:

(seconds) (minutes)

8。 Solution: The distance between the two lanes from the front to the back of the vehicle and the problem are only the search time of two conductors. Is it used to satisfy: (120 +60)? (15 +20)= 800 (seconds).

People think that when the train passes by, they are far from being conductors. Through time (10 second), the speed difference of the train is obtained. The distance between this speed difference and people's walking speed (90 meters) is divided by the speed of the train.

90÷10+2 = 9+2 =11(m)

A: The speed of the train is 1 1 meter per second.

10。 It takes a few minutes for A and B to meet. We must find out the distance between A and B, and the relationship between their speed and related moving trains. Its speed can be known from the distance between the A train and the B train. So, you must get it. The speed ratio between A and B is at least difficult to determine, and this speed ratio is gradually defined: ①

Relationship, determine the speed of a train, the speed of b, the length of this group of trains is l, which is an 8-second process:

(A) the train started to grasp the problem:

Therefore, B( 1)

(2) training for about 7 seconds, in this process, encounter: encounter.

So (2)

( 1),(2):

(2) the distance between the locomotive armor b:

Meet on the train.

③ Find the distance from the locomotive to BA and B ..

In the case of a locomotive, after (8 +5×60) seconds, event B is in front of the locomotive, so the distance between two locomotives B, A and B is:

(4) How many minutes will A and B meet?

(seconds) (minutes)

B and I will meet in a few minutes.

answer the question

1 1。 1034 ÷ (20-18) = 91(seconds)

12。 182 ÷ (20-18) = 91(seconds)

13。 288 \8- 120 \60 = 36-2 = 34 (m/s)

The speed of the train is 34 meters per second.

14。 (600+200) 10 = 80 (seconds)

A: It takes 80 seconds for vehicles entering the tunnel from front to back to leave the tunnel.

Average problem

1 。 In the final exam, Chinese cabbage scored an average of 89 points in politics, Chinese, mathematics, English and biology. The average score of politics and mathematics subjects is 9 1.5. The average score of subjects such as Chinese and English is 84. The average score of politics and English is 86, and English is above 10. What should be the scores of all subjects in the Chinese cabbage exam?

2。 B two cotton fields, the average yield of seed cotton 185 kg. The average yield of seed cotton in five mu cotton field is 203 kg, and the average yield of seed cotton in B cotton field is 170 kg.

3。 Given the sum of 8 consecutive crown odd numbers 144, find 8 consecutive crown odd numbers.

Every kilogram of 8.8 yuan and 7.2 yuan, 5 kilograms of ethyl sugar, white sugar, white sugar. B Is the price of mixed sugar the same as that of a kilo of sugar in 8.2 yuan?

5。 I bought five sheep in the canteen, and took out two general weights at a time, and got 10 different weights (kg): 47, 50, 565, 438+0, 52, 53, 54, 55. These five sheep, 57, 58, 59. How many kilograms do you need each?

Arithmetic column

What is 1995 according to the number of legal strings here?

Answer: 2, 5, 8, 1 1, 14 ... from France: this is a arithmetic progression, the first term is 2, and the tolerance is 3, so the natural number 1995 1 is 2+3 * (.

2 100 is an indivisible number. What is it?

A: We found that: 1, 2, 3, 4, 5, 6, 7, ..., 1 group, every three numbers, the first two digits of each group can not be divided by the best, 2, 100 group, there is100 ÷.

3, 1988 has 28 consecutive even numbers, even if one of them is the largest number?

Answer: 28 symmetric numbers are even numbers divided into 14 groups, and one group is the smallest and largest group, each group is:1988 ÷14 =142, and the tolerance between the minimum number and the maximum number is 28-1=.

4. Integer greater than 1000. After finding all 34, what is the sum of these numbers except that the supplier and the remainder are equal?

Answer: Because 34× 28+28 = 35× 28 = 980.

34×29 +29 = 35×29 />34×30 +30 = 35×30

34×3 1 +3 1 = 35×3 1

34×32 +32 = 35×32

34 33 +33 = 35×33 BR/> The sum of the above is 35× (29+30+31+32+33) = 5425.

5. A box contains 1, 2, 3... 134 135 red cards. Each card works from any number of cards in the box. Divide the remaining part by each number in the number of 17 cards, and then write the remaining part into another yellowcard and put it back in its original place.

Answer: Because it is difficult to grasp a certain number of times at a time, we might as well consider it as a whole, and then retreat to the simplest situation analysis: suppose there are two numbers 20 and 30, divide by 17 to get the number of yellow cards 16, calculate 3 and 13 respectively, and then calculate 3 and 13 respectively. If the number of yellow cards is still 16, regardless of the sum of a number, the sum is divided by 17, and the rest remains unchanged. Back to the theme1+2+3+...134 135 =136×138.9180 ÷ 17 = 50.

6. The following formulas are arranged according to law:

1+ 1+3,3+5,4+7, 1+9,2+ 1 1,3+ 134+ 15, 1.

Answer: Make clear the law first: each equation has two numbers, the first number is 1, 2, 3, 4 cycles, and the second number is 1 consecutive odd numbers. Since 1992 is even, the two addends of the second one must be odd, so the first one is odd, so it is 1 or 3. If it is 1, then the second number is1992-1=1965438+. 199 1 annual market value (1 991+1) ÷ 2 = 996, and1is always odd, so the equation is1989 =/.

7. As the picture shows, the last two lines are arithmetic progression. What's the difference between these two figures? In the same column, how many tables are the smallest?

Answer: Calculate their differences from left to right: 99992985..., 12,5. Calculate their differences from right to left: 1332, 1325, 13 18, respectively.

Equation 8, 19:

What are the results on the left and right sides of equation 19?

Answer: Because the left and right sides are equal, we might as well just consider the left side to solve two problems: How to spend the equation of the number 18? Species have the formula17 = 3918 5+7+9+... 19+39 = 396.397. What is the number? The number of species on the left is 3, 4, 5, ... 193+1×18 = 21,so the result of19 formula is 397+398+399+...+4/.

9, two numbers are well known: 2, 5, 8, 1 1, ... 2 +(200- 1); 5,9, 13, 17,......5 +(200 - 1)×4。 Do they represent the same number of columns and data?

A: It is easy to know that the first number is 5. Note that in the first series, the tolerance is 3 and the tolerance in the second number is listed. In other words, the second pair of savings 5 is a multiple of 3 and also a multiple of 4. Therefore, in order to convert the demand into five materials, the number of materials with a tolerance of 12 is 5,17,29. The second series is at most 5 +(200- 1)×4 = 80 1. The new series cannot exceed 599, and 5+ 12× 49 = 593, 5+ 12× 50 = 605, so there are 50 pairs in a * * *.

10, as shown in the figure, the side length of the triangle with the bottom is 1 m, and there is a point every 2 cm from each side of the vertex, and then these points are the endpoints. Parallel to this, the production line will be an equilateral triangle, divided into many small equilateral triangles with a side length of 2 cm. Find (1) a few equilateral triangles with a side length of 2 cm, and (2) the total length of parallel lines.

Answer: (1) From top to bottom, there are 100÷2 = 50 lines, 1 line and the second line of the third line, the last line of the third line, 5, ..., 99, so the total is (1 99. ⑵ There are 49 parallel segments in three directions, which transmit * * * in the same horizontal direction, the first two centimeters, the fourth centimeter, the sixth centimeter, ..., and the last one is 98 centimeters, so the total length is (2 +98)× 49÷2×3 = 7350 centimeters.

1 1, the factory is busy with work in June +0 1 instead of having a rest on Sunday. From the first day, the same number of workers were sent from the factory to the factory every day. Until the end, there were only 240 workers left in the factory. If the final statistics show that the workload of production workers is 8070 days (one day's work) and they are not absent from work, how many workers will the factory arrange to go to work this month?

A: There are 30 days, 1 1 month. The significance of the problem is that the number of plants is decreasing every day, and the last 240 people and everyday people form a arithmetic progression. According to the nature of arithmetic progression, the sum of the first day and the last day is equal to 8070÷ 15 = 538. On the first day, workers are paid 538-240 = 298 (298-240) per day.

12, Xiao Ming read an English book. On the first day of reading, he read it 35 times and 5 times a day. On the last day of reading, they read only 35 times and 45 times a day. Compared with the first and last day of the previous trading day, he can only read 40 readings. How many pages are there in this book?

A: The first scheme: 35, 40, 45, 50, 55...35; The second scheme: 45, 50, 55, 60, 65, ... 40 times; The first scheme: 40, 45, 50, 55, ... 35+35./p > The second scheme: 40, 45, 50, 55, ... (the first day of the last day), and the second program must be 40, 45, 50, 55, 60, 65, 70***385.

13,7 The small fleet planted 18 trees and 100 different lineups. Check numbers are different, including planting trees in the team. How many trees have the tree planting team planted at least?

Answer: We all know that the other six teams planted 100- 18 = 82, in order to make Ru vulgar men "and value Ne furry to pay for plastic?" Stamp? It should be better:17+16+15+14+13 = 75, and the minimum lineup is 82-75 = 7.

14 mutually different natural numbers are arranged from small to large into a known sum 170. If you delete the largest number and the smallest number, the remaining sum is 150. What is the second number in the original order?

A: The maximum and minimum maximum numbers are 170- 150 = 20, so when 20- 1 = 19, The maximum number is19+18+17+16+15+14+6543818+/kloc-0.

circulate

Basic exercises

1,(1) ○△□□□□□□□□ ... 20 Graphics (□)(2) Article 39

(sunspot).

Xiaoyu practices calligraphy. If she writes 60 words repeatedly, she should write (big).

(1) Join the tug-of-war team of senior three students. Their competition order in a team is 26 students (male students), three men and two women.

4, there is a number: 1, 3,5, 1, 3,5, 1, 3,5 ... 20, and the number 20 is (58).

The total number of five-star red, white and black beads is the same as that of 100, and it is ranked as white 1 black according to the requirements of 3 red and 2.

(1), 52 (white) beads.

(2) The first 52 beads are * * (17) white beads.

6. A asks B: Today is Friday, and it is 30 days a week (Sunday).

B Q A: If 16 is a Monday, the week of 3 1 this month (b).

Monday, May 1 2006, Sunday, 28th of this month.

A, B, C and D 4 playing cards, with 54 playing cards in the middle and 37 cards up and down. "King"? ※? I think I have grasped poker confidently, and I finally caught the "king". Do you know how C works? (37÷4 = 9 ... The first person to get the license plate must catch "Wang")

1,( 1)□。

(2) sunspots.

2 big

Three male students.

4, 20(3), 20 numbers, and (58).

(1) 52 (2) * * 52 beads (17) pearl white (white) balls.

Article 6, paragraph 2.

(37 ÷ 4 = 9 ... The first person to get permission must catch "Wang". ※

Improve the practice of 1, (1) ○△□□□□□□□□ ... 20 The chart is (□).

(2)○□◎○□◎○□◎○。 ..... 25 graphics card (○).

There is a row of colorful flags in the stadium, with "three reds, one green, one yellow and one last time (green sign)" arranged on 34 sides. BR/>； 3. "Love mathematics since childhood, love mathematics since childhood ..." For 33 words (love)

The students of Class 4 (1) participated in the tug-of-war competition in the school. Their teams were arranged by three men and two women in turn. "There are 26 students (male students) in one team.

5: 1, 3,5, 1, 3,5, 1, 3,5 (3) 20 and 20 (58)

A asks B: Today is Friday, and it will be Sunday in 30 days.

BQA: If it's Monday, 16, Monday of this month, 3 1, that's a week (b).

Monday, May 2006 1 day, Sunday, 28th of this month.

A, b, c and D 4 play cards. There are 54 cards with the "King" plug-in from top to bottom, with 37 cards in the middle. C thinks it is safe to catch poker first and "king" last. Do you know that c is calculated?

* 37÷4 = 9 ... 1 (You must catch "Wang" when you draw first)

answer

1,( 1 )"。

(2)○

"green sign"

3. Love.

4. (1) Male students.

5, the twentieth (3), the twentieth (58)

6th (Sunday) (B)(DD)

* 37÷4 = 9 ... 1 (the first person to get the license must catch up with Wang).

/a & gt；

Decimal calculation speed and simple calculation (b)