Primary 5 liter 6 Olympiad math questions, 5 liter 6 grade Olympiad math questions

You can't use equations in elementary school math. Then I gave an analysis.

Analysis: The time it takes for C to take this part of the road is the time it takes for A to send B to a place and then turn back to pick up C, which is 8 3 hours.

During this time, A traveled a total of 36 * 8 3 = 96 km, and the distance from A to the intermediate point (where A put down B) is (96 + 8) 2 = 52 km.

It's easy to understand by making a simple diagram.

When A meets C, B walks some distance again. The time it takes for A to go from putting down B to meeting C is: (52-8) 36=11 9 hours. The distance traveled by B is: 4*11 9=44 9 km.

Then the problem is reduced to a chase problem. A carries C at a speed of 36 km/h. To chase B, the speed is 4 kilometers per hour. The distance is (52 + 44 9) = 512 9 km. The place where I caught up was the b-place.

Time taken to catch up: (512 9) (36-4) = 16 9 hours. During this time, C traveled a total of 36 * (16 9) = 64 kilometers on A's motorcycle. Combined with the 8 kilometers traveled by C, the total number of places A to B is 72 kilometers.

Since the two of them departed and arrived at the same time, the journey by car was equal, and the distance on foot was also equal.

Let the distance be x, and the distance B walks is also 8 kilometers, so it is x-8 in the car, and A's journey from putting B down to meeting C is: x-8*2=x-16 Because A has the same time from the departure to the time he meets C, so:

8/3=[（x-8）+（x-16）]/368/3=（2x-24）/36

2x-24=96

x = 60**Bounty Points.

The fraction three-eighths means (), also means (), and also means ().

The sum of the three numbers A, B, and C is 100, A is divided by B, and C is divided by A, all of which give 5 more than 1, and B is a fraction of C? (Multiple choice).

A total of 56 students from the 5th and 6th grades participated in the model aircraft group. Boys make up two-thirds of the students coming from the fifth grade and 75 per cent of the students coming from the sixth gradeThere are as many girls in the fifth and sixth grades as there are.

How many people in grades 5 and 6 participate in the model airplane group?

Mom bought some pears and apples and spent a total of yuan. It is known that the unit price ratio of pears and apples is 4:5 and the weight ratio is 5:7.

For a project, it takes 10 days for Team A to complete it alone, and 15 days for Team B to complete it alone. Now Team A has been doing it alone for a number of days and then Team B has been doing it, and the task has been completed in 11 days. How many days did both teams do it?

The diameter of the outer circle is 18 centimeters, the area of the ring is 105 square centimeters, how many square centimeters is the area of the inner circle?

1 The fraction three-eighths means (3 divided by 8), also means (3 to 8), and also means (3 eighths).

2 The sum of the numbers A, B, and C is 100, and A is divided by B, and C is divided by A, and 5 is more than 1, and B is a fraction of C.

A is 16, B is 3, C is 81, B is 1/27 of C, choose D

3 Since one-third of the fifth-grade is equal to one-quarter of the sixth-grade (both girls), the ratio of fifth- to sixth-grade students is 4:3, so that fifth-grade students have 56 times 4 7 = 32 (persons) and sixth grade has 56-32 = 24 (persons).

4 The total price ratio of pears and apples is 4 times 5:5 times 7 = 4:7, so it costs to buy pears multiplied by 4 11 = 6 (yuan), and apples cost yuan).

5 1 = 1 10 times 8 + 1 15 times 3, team A did it alone for 8 days, and team B did it alone for 3 days.

6 (18 divided by 2 squared by centimeters).

1. Since the three people set off and arrived at the same time, A took B to walk for a while, put B somewhere, came back to pick up C, and then B continued to walk, and the three arrived at the same time.

Since the two of them set off and arrived at the same time, the journey by car was equal, and the journey on foot was also equal.

Set the distance is x, and the distance that B walks is also 8 kilometers, so the car is x-8 A from putting B down to meeting C The journey is: x-8*2=x-16 Because A asked Jianling to meet C from the time of departure, the time of the two was the same, so:

8/3=[（x-8）+（x-16）]/368/3=（2x-24）/36

2x-24=96

x = 60**Bounty Points.

15 people process: Yuying School Numbers: 35x+15 Yuhong School Students: 35y+20 **Total: (35x+15)*(35y+20).

35xy+20*35x+15*35y+15*2035xy20*35x

15*35y

It is all a multiple of 35, 15 * 20 = 300300 = 35 * 8 + 2035 * 8 is also a multiple of 35, and the remaining 20 people use 35 sheets of film (35-20), that is, 15 people.

After the last time A takes out two-sevenths of the last time, there is 155 left, then A has 155 * (7 5) = 217 before the third distribution.

62 to C.

In the same way, it is known that before the third split, B has 136 * (11 10) deferred matches.

136* (1 10) to C.

And before the third distribution of C, there were 209-62-136* (1 10).

In order to ensure that at least one number of children can get two apples, the slow train travels 37 kilometers per hour, after 16 hours, divided by 2, the teacher has to take (

Give an apple to the children.

7) Xiao Ming has 20 stamps (1) a number plus 3, minus 2, multiply 5, 80 people signed up for the sports group, 160 people participated in the art group, and both the sports and art groups participated in (

Person. 4) There are 3 trains, 4 liners, and 2 planes from A to B.

3) There are 200 students in the fourth grade, which is equal to 10, and this number is (2) There are 5 Wednesdays in March of a certain year, and 4 stars are related to the second period, and the first day of October of this year is the week (, and the two cars are separated by each other

Kilometer. 6) There are 35 children in the kindergarten class, and there are a total of different allergy walks.

5) Two cars depart from A at the same time, running opposite to each other, and the express train travels 43 kilometers per hour.

The answer is five days. And the answer looks at the process: A can complete the project every day in the round cave hall 1 8

B tremor mill can complete 1 10 of the works per dayC can complete the works of 1 15. Therefore, A and C can complete the project in 3 days 1-3 (1 8 + 15) = 1 2

So the rest is done by B, just divide 1 2 by 1 10 equals 5 days. Tachibana.

15 people process: Yuying School Numbers: 35x+15 Yuhong School Numbers:

35y+20 **Total: (35x+15)*(35y+20) =35xy+20*35x+15*35y+15*2035xy 20*35x 15*35y, all are multiples of 35, 15*20=300300=35*8+20, 35*8 is also a multiple of 35, and the remaining 20 people are left with 35 sheets of film, that is, 15 people.

There seems to be a problem with the last question, I'll eat first, and I'll give you the process later.

1. Imagine that after each person shakes hands once, immediately draw a horizontal line under the person's name, which is called a person. Because each handshake is between two people, each handshake is drawn under each person's name, increasing the number of people by 2. It can be seen that no matter how many times you shake hands, you can be sure that the total number of handshakes must be even.

Temporarily divide these people into two factions: those who have held hands odd times belong to the odd faction; A person who has held an even number of hands belongs to the even school.

A person who has held an even number of hands will certainly have an even number of people under his name. The sum of several even numbers is still an even number. Therefore, the sum of all the people of the even faction must be an even number.

And because the odd number of people = the total number of people - the number of even people, the even number minus the even number, the result is still an even number. Therefore, the number of people in Qipai must be even.

However, the number of people under each name of Qipai is an odd number. Odd numbers add up or odd numbers, only the addition of even odd numbers can give even numbers. Therefore, people who have shaken hands an odd number of times must have an even number.

2. N lights are on at the beginning. Each light turns off after an odd number of pulls, and lights up again after an even number of pulls. Discussed in two cases:

1. When n is an odd number, (n 1) is an even number.

To turn off all lights, each light must be pulled an odd number of times, the sum of an odd number of odd numbers is an odd number, and the total number of times n lights pull the switch must be an odd number;

Each time (n1) switches are pulled, (n 1) is an even number, no matter how many times you pull, the sum of any number of even numbers is an even number, and the total number of times you pull the switch can only be an even number.

So when n is an odd number, according to the regulations, all the lights cannot be turned off.

2. When n is an even number.

As shown in the figure below, the white dot means the light is on, the black dot means the light is off, and each time (n 1) lights are pulled, there is a light at the junction of black and white that is not pulled:

At the beginning:

First time:

Second time:

The third time:

Fourth:

Fifth time:

Sixth time:

Looking at the diagram above, you can see that when n is an even number, you can turn off all n lights by pulling (n) 1 lamp each time and pulling n times for n.

After a brief look at the problem, it is basically the same type, and to be honest, it is the easiest to list binary equations.

1. The two water pipes of A and B are opened separately and filled with a pool of water, which takes 20 hours and 16 hours respectively. If the pool is empty, open the two water pipes A and B at the same time, and after 5 hours, open the drainage pipe C, and ask how many hours it will take for the pool to be full?

Answer: 1 20 + 1 16 9 80 indicates the work efficiency of A and B.

9 80 5 45 80 indicates the amount of water coming in after 5 hours.

1-45 80 35 80 indicates the amount of water that is still needed.

35 80 (9 80-1 10) 35 means 35 hours to fill up.

A: After 5 hours, it will take another 35 hours for the pool to be full.

To repair a canal and repair it alone, it takes 20 days for Team A to complete and 30 days for Team B. If the two teams cooperate, due to the impact of each other's construction, their work efficiency will be reduced, the work efficiency of team A is four-fifths of the original, and the work efficiency of team B is only nine-tenths of the original. Now that the canal is planned to be completed in 16 days, and the number of days required for the two teams to work together is as few as possible, how many days will the two teams have to work together?

Answer: From the question, the ergonomics of A is 1 20, the ergonomics of B is 1 30, and the cooperative ergonomics of A and B is 1 20*4 5+1 30*9 10 7 100.

And because it is required that "the number of days for the two teams to cooperate is as small as possible", it should be done more by A who does it fast, and only those who are too late within 16 days should be allowed to cooperate with A and B. This is the only way to "have as few days as possible for the two teams to work together".

If the cooperation time is x days, then the time for A to do it alone is (16-x) days.

1/20*（16-x）+7/100*x＝1

x 10 A: A and B have a minimum of 10 days of cooperation.

3. On the highway, a three-meter-long car outweighs a 17-meter-long truck with a speed of 110 kilometers per hour at a speed of 110 kilometers per hour. How many seconds does it take for a car to overtake a truck?

Answer: 17 + 3 = 20 (m).

1 50:1 360 = seconds).

1.The circumference of the wheel must be proportional to the distance traveled and the number of revolutions of the wheel.

2.Divide a cone into two parts of the same volume and shape along the diameter of the ground, and the surface area is increased by 96 square centimeters, the height of the cone is 6 centimeters, and the volume of the cone is ( ) cubic centimeters.

3.The Anti-Japanese War Memorial Hall received 2,600 visitors in 5 days, according to this calculation, how many people received in late August?

4.A pool is equipped with two water pipes A and B, and the empty pool can be filled in 20 minutes by opening the water pipe alone, and the whole pool can be drained in 30 minutes by opening the water pipe of B alone. If two pipes are left open at the same time for a few minutes, can you fill two-thirds of the entire pool?

5.A house needs to be paved with square bricks, and 96 square bricks with a side length of 3 cm are needed. If you use a square brick with a side length of 4 cm, how many will you need? (Proportional solution).

Answer: 1Distance traveled = wheel circumference * number of revolutions, so they are proportional.

Number of wheel revolutions = stroke of the wheel circumference, so they are inversely proportional.

2.From the bottom surface, there are two more bottom areas. So the base area = 96 2 = 48 (square centimeters).

So he has a volume of 48*6=288 (cubic centimeters).

3.Because it receives 2,600 visitors in 5 days, it receives 2,600 visitors 5 or 520 visitors per day. There are 11 days in late August, so it can accommodate 520*11=5720 (people).

4.Open at the same time for x minutes to fill two-thirds of the full pool.

x(1/20-1/30)=2/3

Solution x=40

A: If two pipes are left open at the same time for 40 minutes, two-thirds of the total pool can be filled.

5.Set up x blocks.

4x=96*3

x=72A: 72 blocks are required.