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Solving problems in Olympic mathematics in primary schools
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1. There are two trains, one is102m long, and it runs 20m per second. The length of the train is120m, and it runs at the speed of17m per second. Two cars are driving in the same direction. How many seconds does it take from the first train to catch up with the second train to the departure of the two cars?

2. Someone walks at a speed of 2 meters per second. A train came behind, which took 10 seconds longer than him. As we all know, this train is 90 meters long. Find the speed of the train.

At present, two trains run in the same direction at the same time. 12 seconds later, the express train overtook the local train. The express train runs18m per second, and the local train runs10m per second. If the tails of two trains are flush and driving in the same direction at the same time, the express train will overtake the local train after 9 seconds. Find the body length of two trains.

4. It takes 40 seconds for a train to cross a 440m bridge and 30 seconds for a 3 10/0m tunnel at the same speed. What is the speed and body length of this train?

Xiaoying and Xiao Min took two stopwatches to measure the speed and length of the passing train. Xiaoying used her watch to record that the time that the train passed in front of her was 15 seconds. Xiao Min used another watch to record that it took him 20 seconds to cross the first telephone pole in front and the second telephone pole in the back. It is known that the distance between two poles is 100 meters. Can you help Xiaoying and Xiao Min calculate the total length and speed of the train?

6. It takes 40 seconds for a train to cross a 530-meter bridge and 30 seconds to cross a 380-meter cave at the same speed. Find the speed and body length of this train.

7. The two started from two places along the path next to the railway line and walked at the same speed. A train came, 10 seconds. The whole train passed by A. Three minutes later, B met the train, and the whole train only took 9 seconds to pass by B. How long did the train leave B before they met?

8. Two trains, one with a length of120m and a speed of 20m per second; The other train is160m long and runs at a speed of15m per second. The two cars are driving in opposite directions. How many seconds does it take from the front meeting to the back leaving?

9. Someone walks at a speed of 2 meters per second. The train overtook him from behind 10 seconds. As we all know, the length of this train is 90 meters. Find the speed of the train.

10. Party A and Party B walk along the railway at the same speed. It took 8 seconds for a train to pass by Party A, and only 7 seconds to pass by Party B after leaving Party A for 5 minutes. How many minutes after Party B met the train?

Second, answer the question.

1 1. Fast train length182m, traveling 20m per second, slow train length1034m, traveling 8m per second. The two cars are parallel in the same direction. How long does it take for the express train to cross the local train when the rear of the express train meets the rear of the local train?

12. The length of the express train is182m, the length of the local train is1034m, and the speed of the local train is18m per second. The two cars are parallel in the same direction. How many seconds can an express train pass through the local train when the heads of the two cars are aligned?

13. A person is running along the railway at a speed of 120 meters per minute. A 288-meter-long train came from the opposite side. It took him 8 seconds to find the speed of the train.

14. A train is 600 meters long. It passes through a 200-meter-long tunnel at a speed of 10 meter per second. How long does it take to leave the tunnel from the front to the rear? First, multiple-choice questions:

1, which belongs to the linear equation in the following categories is ().

A.5a+4b B.4x+9x

C.5x2+9y2 D. 7a-4b

2. The solution of equation 3x-2=-5(x-2) is ().

A.- 1.5 b . 1.5 c . 1d .- 1

3. If the solution of the equation about satisfies the equation, the value of is ().

A. 10 8th century BC.

4, according to the following equation property is correct ()

A. Fuck, get B. Fuck, get

C. pass, get D. pass, get

5. When solving the equation, after removing the denominator, the correct result is ()

A.B.

C.C.

6. The price of TV sets has been reduced twice in a row 10%. After the price reduction, the price of each TV set is one yuan, so the original price of TV set is ().

A.0.8 1a yuan B. 1.2 1a yuan C. 1. 1a yuan D.0. 1a yuan.

8. A store sells two pieces of clothes, each 60 yuan, one earns 25% and the other loses 25%. Then after these two clothes are sold, the store is ().

A. Don't earn or lose B. Earn 8 yuan C. Lose 8 yuan D. Earn 8 yuan

9, in the following equation, belongs to the linear equation is ().

(A) (B) (C) (D)

10, the solution of the equation is ()

(A) (B) (C) (D)

1 1, given the equation, the following equation may not be true ().

(A) (B)

(C) (D)

12, the solution of the equation is that it is equal to ()

(A) (B) (C) (D)

13, solve the equation, remove the denominator, and get ()

(A) (B)

(C) (D)

14, the following equation variation, the correct is ().

(1) Equation, shift term, get

(b) Equation, without brackets, gives

(c) Equation, which converts the unknown coefficient into 1 to obtain

Formation of equation

15. Son 12 years old, father 39 years old. The father is four times as old as his son.

(a) Three years later; (B)3 years ago; Nine years later; No way.

16. The football used by chongqing lifan New Feeling Football Team for training is made of 32 pieces of black and white cowhide, of which the black leather can be regarded as a regular pentagon and the white leather as a regular hexagon. The ratio of black and white leather blocks is 3:5, and the number of black and white leather blocks is required. If the number of black leather blocks is 0, the listed equation is correct ().

(A) (B)

(C) (D)

17, Coral Middle School built a comprehensive building, leaving a rectangular open space with a length of more than 5m and a circumference of 50m. In order to beautify the environment, the school decided to plant it as turf. It is known that the minimum planting cost per square meter of turf is RMB, so planting turf needs at least ().

(1) Yuan; (b) yuan; (c) yuan; (4) yuan.

One year, two years, three years.

2.25 2.43 2.70

18. The annual interest rate of bank education savings is shown in the following table:

Xiaoming is in grade seven now. In July this year, his parents deposited 30 thousand yuan in the bank for him to use when he was in high school three years later. After three years, the income will be maximized, and Xiao Ming's parents should adopt ().

(a) Direct deposit for three years;

(b) Deposit first 1 year, and after 1 year, the total interest will be automatically transferred to the 2-year period;

(c) Deposit one 1 year, and after 1 year, automatically transfer the principal and interest to two 1 year;

(d) Deposit a 2-year deposit first, and after 2 years, the total interest will be automatically transferred to 1 year deposit.

Third, fill in the blanks:

1, then _ _ _ _ _.

2, known, then _ _ _ _ _ _ _.

3. If the solution of the equation is 3, the value of is _ _ _ _ _ _ _ _.

4. If there is a three-digit number, its unit number is, the number on the tenth digit is, and the number on the hundredth digit is, then this three-digit number is expressed as _ _ _ _ _ _ _ _ _ _ _.

5. There are 96 people in Class A and Class B, and Class A has 2 more people than Class B, so Class B has _ _ _ _ _ _ _ _.

6. Three times a number is twice as big as half of it. If a number is, the column equation is _ _ _ _ _.

7. When _ _ _ _ _ _ _ _ _, the values of algebraic expression and are opposite.

8, formula, known, then _ _ _ _ _.

Day one two three four five six

1 2 3 4 5 6

7 8 9 10 1 1 12 13

14 15 16 17 18 19 20

2 1 22 23 24 25 26 27

28 29 30 3 1

9. As shown on the right, it is the calendar of 65438+February 2003. At present, four numbers are arbitrarily framed by a rectangle in the calendar.

Please use an equation to express the relationship between _ _ _ _ _ _ _ _ _ _ _ _ _.

10, a long cylindrical test tube with an inner diameter of 3㎝, which is filled with water. Now gradually drop the water in the test tube into a cylindrical glass with an inner diameter of 8㎝ and a height of 1.8㎝. When the glass is filled with water, the water in the test tube drops _ _ _ _ _.

1 1. During the National Day, New Century Department Store has a seasonal discount. Jian Shuang bought a sportswear at a 20% discount, saving 16 yuan, so he actually spent _ _ _ _ _ _ yuan on this dress.

12, the total length of chengdu-chongqing railway is 504 kilometers. An express train departs from Chongqing at a speed of 90 kilometers per hour. 1 hour later, another local train departed from Chengdu at a speed of 48 kilometers per hour. Then these two trains leave at the local train _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

13. When we were young, we heard the story of the race between the tortoise and the hare. We all know that the tortoise finally defeated the white rabbit. If in the second race, the white rabbit is ashamed and brave, and catches up with the tortoise at the speed of 10 1 m/min when it is behind the tortoise, and the tortoise still crawls at the speed of 1 m/min.

14. The annual interest rate of one-year time deposit is 1.98%, and 20% interest must be deducted for withdrawal at maturity and turned over to the state treasury as interest tax. If Xiaoying deposits a one-year time deposit, she will get interest of 158.4 yuan after deducting interest tax at maturity, then the RMB she deposits is _ _ _ _ _ _ _.

15, 52 cars lined up in two teams, each car was one meter long, and the distance between the two cars was 3a/2m. The average speed of the team was 50 meters per minute. It takes 16 minutes for this train to pass through the 546m long square, so a = _ _ _ _ _ _ _