Grade 6 Olympiad with method, process, answer .

Passenger car speed * 2 hours = truck speed * 3 hours.

So the speed of the passenger car and the speed of the van = 3 2

Therefore, when the two cars meet, the passenger car has gone 3 5 of the whole distance, and the truck has taken 2 5 of the whole distance and 30 kilometers = the whole distance * (3 5-2 5) = the whole distance * 1 5 so. The whole distance is the distance between the two places = 30 kilometers * 5 = 150 kilometers. Oh also.

Passenger car speed: truck speed = 3:2

Speed difference between two cars: sum of two car speeds = 1:5

In the same time (the two cars complete the whole process together, that is, use the speed of the two cars and complete the whole process) the speed difference between the two vehicles * time: the speed of the two vehicles and * time = 1:5 The former = 30 then the latter = 30 * 5 = 150

Let the speed of the passenger car be x, the speed of the truck is y, the whole journey is z, and the meeting time is tz=2x=3y x=3 2y

tx+ty=z t(x+y)=z t(3/2y+y)=3y t=6/5

tx-ty=30 t(x-y)=30 6/5(3/2y-y)=30 y=50

So z=3y=150 km.

The two places are located at a distance of s km.

Bus speed: s 2; Wagon speed: s 3 formula: speed = distance time.

Let the time it take for the two cars to meet is t

s 2)t+(s 3)t=s When two cars meet, the sum of the distances traveled by the two cars is the total distance.

Get t = 6 5

s 2) t-(s 3) t = 30 The passenger car travels 30 kilometers more than the van.

You can ask for this step yourself.

If you are not familiar with this type of problem, you can use the method of drawing to assist your thinking, generally using the formula: speed = distance time. Look for the equation.

Let the distance x meet the time t, the passenger car speed is x 2 and the truck speed is x 3, then (x 2) t (x 2) t x; (x 2 x 3) t 30 gives the distance between the two places to be 150 km.

It takes 2 hours for buses and 3 hours for trucks.

V passengers: V goods = 3:2

v customer * t: v cargo * t = 3:2

v passenger * t - v cargo * t = 30

V passenger * t + v cargo * t = 150

The two places are 150 kilometers apart.

The two places are located at a distance of x kilometers.

x 2 = bus speed.

x 3 truck speed.

x (x 2 + x 3) = time from start to time of meeting 6 5 Passenger cars travel more (x 2-x 3) x 6 km per hour than trucks.

x/6)*(6/5)=30

x=150

1.Solution: According to the title, you can get:

888÷a……a； 518÷a……a+7； 666÷a……a+10 with the intermediate equation (518 a......a+7), then the dividend of the first equation should be added to 7, and the dividend of the third equation should be subtracted by 3 (10-7=3) to calculate the difference between 895 (888+7=895) and 518 and the difference between 663 (666-3=663) and 518, which is the greatest common divisor (factor) of 29

The final answer is 29

Answer: This natural number is 29

2.From the title: he has a total of 512 different ways to eat;Here's why:

After each piece, there are two options: keep eating and eat tomorrow;

According to the principle of multiplication, there are a total of 2 to the 9th power, that is, there are 512 ways to eat.

3.Solution: Derived from the question:

10 500 (yuan).

12 500 (yuan).

then the profit is: (12-10) yuan).

Answer: Mr. He made a total of yuan in this batch of **.

4.Solution: Suppose: It takes X and Y days for Team A and Team B to complete the task alone.

From the title: (1 x + 1 y) 24 = 1

6\x+4\y=1\5

Solution: x=60, y=40

It is verified that x=60 and y=40 are the solutions of the original fractional equations.

Teams A and B need 60 and 40 days to complete the task alone.

5.I'm sorry, I can't answer this kind of question, and I can't draw a graph, I'm sorry.

I hope the above four questions are helpful to you......）

1.Arrange the 9 numbers from 1 to 9 in a row so that the second number is divisible by the first, the third number is divisible by the sum of the first two numbers, and the fourth number is divisible by the sum of the first three numbers. The ninth number is divisible by the sum of the first eight numbers, if the first number is 6, the fourth number is 2, and the fifth number is 1, what is the last number?

Analysis: Since the first number is 6, the second number can only be 2 or 3, and since the fourth number is 2, it can only.

is 3, since the sum of the first two numbers is 9, then the third number can only be 3 or 9, obviously it can only be 9.

In this way, if the sum of the first five numbers is 21, then the sixth number can only be 3 or 7, obviously only 7, and since the sum of the first six numbers is 28, then the seventh number can only be 2 or 4 or 7, obviously it can only be 4.

So that the sum of the first seven numbers is 32, then the eighth number can only be , and obviously can only be 8.

This way the ninth number can only be 5.

2.Starting with 1, write 1234 in turn....20032004, What is the remainder of this multi-digit number divided by 9?

Analysis: If there is a remainder between 9 and a number, divide the sum of the digits of the number by 9 to obtain the remainder.

Same. According to this law, the sum of the digits of this number is: 2005*1002=2009010

2009010 the sum of each digit is 12, and the remainder of the original number is 3 when divided by 9, then the remainder of the original number is also 3.

3.If a certain commodity is sold at a reduced rate of 5%, a profit of 6,250 yuan can be obtained; If you sell it by subtracting 25% of the list price, you will lose 1,750 yuan.

The pricing is: (6250+1750) (25%-5%)=40000 yuan.

The purchase price is: 40,000 * (1-5%) - 6,250 = 31,750 yuan.

4.Master Li plans to make a batch of parts, and if he does 10 more parts per hour, he can complete the task 1 hour earlier; If he does 20 more per hour, he can complete the task 1 hour early, and ask Master Li how many parts he plans to make?

, that is, every two pens are 10 yuan more expensive than every two ballpoint pens, that is, a single is 5 yuan, so the ballpoint pen ** is:

95-5*5) (5+5)=7 yuan, and the pen is 7+5=12 yuan.

It would be easier if you could use binary equations, but I don't think I learned the Olympiad in elementary school......This is a solution to an unused equation.

2。It's all over by yourself, and if you don't have a few, just count it right.

3。Three identical three-digit numbers are multiples of 111 111=3*37

So all the natural number combinations are:

Hour 46 minutes is 286 minutes = 45 * 6 + 16 That is, I walked six times, rested six times, and walked the seventh time.

The actual walking time is 40*6+16=256 minutes Since the walking speed increases, the time required to walk back is 256 2=128=30*4+8, so the return time is (30+10)*4+8=168 minutes=2 hours and 48 minutes.

The production speed of the 5a workshop is 600 18=100 3 pieces of tops and 50 pieces of pants per day.

Workshop B produces tops at a rate of 600 15 = 40 pieces per day, and trousers at a rate of 40 per day.

Since B produces tops quickly and A produces pants quickly, it is produced separately first.

And the speed of B production of tops can not keep up with the speed of A production of pants, so B factory specializes in the production of tops, and factory A first produces pants and then produces tops, that is, B = 40 * 30 = 1200 pieces of tops, and factory A only needs 24 days to produce matching pants, and the remaining six days produce tops and pants at the same time, but because of separate production, it only needs to arrange time reasonably. 6 * (3 5) * 100 3 = 120 pieces for tops, and the remaining time to produce pants is 6 * 2 5 * 50 = 120 pieces Just matching, that is, up to 1200 + 120 = 1320 pieces of matching clothes.

Equation solution: 100 3x+40*30=50(30-x) Find x and substitute 50*(30-x).

6。The equations for x, y, and z are 7x=1y+2z, respectively

7y=10z+1x, i.e., 7y-10z=1x is brought to the above equation to get 12y=18z7

1.Let's use binary equations, this should be simpler.

Solution: Set the fountain pen x yuan, the ballpoint pen y yuan.

5x+5y=100-5

7x+3y=100+5

5x=95-5y

x=19-y

7 times 19-7y+3y=105

133-4y=105

4y=133-105

y=7x=12

That's it, let's solve it first, there is not enough time.

1) Set the ballpoint pen to be y and the fountain pen to x

Then the original formula = 5x + 5y + 5 = 100 yuan.

5x+5y=95 yuan.

7x+3y-5=100 yuan.

7x+3y=105 yuan.

105-95=10 yuan.

10 2=5 yuan x-5=y95-(5 5)=70 yuan.

70 (5+5)=7 RMB.

7 + 5 = 12 yuan.

Answer: The fountain pen is 12 yuan, and the ballpoint pen is 7 yuan.

2) Because of the difference between the two sides, then d = h e = ga = 120 50 = 6000

b=112×60=6720

c=104×70=7280

d=96×80=7680

e=88×90=7920

f=80×100=8000

g=e=7920

h=d=7680

Medium f is the largest, so f is the best.

The score is too little, the amount of work is too much, and I am too lazy to do it.

Set the fountain pen and ballpoint pen unit price are x and y yuan respectively.

5x+5y=100-5

7x+3y=100+5

Solve the system of equations – x = 12, y = 7

7. Let ab be S, then according to the time taken by the two people to meet twice, (100+S) (S-100)=(3S+300) (S+300) can get S=300, then 2S=600 is AC

15 questions were answered correctly, 4 were answered incorrectly, and 3 questions were not answered.

I don't know, give a few more points, it's too much work.

I'm dizzy, 6th grade? Shame... If I hadn't done it in the sixth grade, I wouldn't have done it now, and if I were asked to use the knowledge of the sixth grade, I wouldn't be able to do it.

If the distance is x kilometers and the original time is y hours, the original speed is x y kilometers per hour;

Column equation [x (x y)+2] y=7 8x (x y-2)]-y=2 3

Solving the system of equations yields x=56

The second question, if the first question can be understood, the second question is the same.

I'd also love to see that the sixth-grader can solve this problem with his elementary school knowledge.

Let the distance between a and b be x km.

Then A travels 1 4x km and B travels (1 2x-60) km.

This results in 2:3=1 4x:1 2x-60

The solution is x=480

My skills haven't reached such a high level.,I can't understand the wordless book yet.。。。

There is a prerequisite for this question, A and B have the same velocity.

Take the length of the train as 1

The speed difference between cars and people is 1 8

The speed of the car and the person is 1 to 7

Vehicle speed: (1 8 + 1 7) 2 = 15 112 Human speed: (1 7-1 8) 2 = 1 112

When the car leaves A, the distance between A and B is equal to the distance between the car and B plus the length of the car is: (15 112 + 1 112) 5 60 + 1 = 307 7 A and B meet and need: 307 7 (1 112 + 1 112) = 2456 seconds from the car meets B, to A and B meet, need:

2456-5 60 = 2156 seconds.

Set: x meters per second for trains, y meters per second for people.

8x-8y=7x+7y

x=15y5 minutes 300 seconds.

300x-300y+7x+7y=300*15y-300y+7*15y+7y=4312y

4312y (y+y) = 2156 seconds.

2156 seconds = 35 minutes and 56 seconds.

【Answer】The ratio of the speed difference between the speed of the driver and the speed difference between the driver and the driver is 8:7, and the speed difference is 7 parts, and the speed sum of the person is 8 7 1 parts, then the speed difference is 7 times the speed of the person, and the time when the two meet is 7 times the time when the car person pulls apart, and the time when the two meet is 5 minutes and 8 seconds 7 35 minutes and 56 seconds.

According to (speed and + speed difference) 2=fast; (speed and - speed difference) 2 = slow speed, you can know that the speed of the train is (1 7 + 1 8) 2 = 15 112 train length.

The speed at which A and B walk is (1 7-1 8) per second 2 = 1 112 train conductors.

Therefore, the speed of the train is 15 times the speed of a human walk.

When the train passes by A and then by B, it takes 5 minutes, and it takes 5 * 15 = 75 minutes to walk by a person.

Since A also walked towards B for 5 minutes during this time, the distance between A and B was 75-5=70 (minutes) when the train passed by B.

A and B are at the same speed and walk in opposite directions, so it only takes 35 minutes.

2.Solving tricks.

A and B traveled in the same direction along the railway, and it took 8 seconds for a train to pass by A. 5 minutes later, it took 7 seconds to drive past B, how many minutes will it take for the two to meet?

Analysis: The key to solving this question is 1The train is traveling in the same direction as A, and the length of the person is usually negligible, so if the train passes through A in 8 seconds, it means that the train in 8 seconds travels one more length of the train body than A; After 5 minutes, he met B and drove past B in 7 seconds, indicating that the train and B were traveling in the same direction, and after 7 seconds, the train and the person traveled a total of one body length.

According to the length of the body, the multiple relationship between the speed of the train and the speed of the person walking must be solved. 2。The train met B 5 minutes later, and now the distance between A and B is equal to the distance traveled by the train in 5 minutes minus the distance traveled by A in 5 minutes.

Finally, according to the distance between A and B and the speed between the two people, find the meeting time that needs to be used.

Untie; The speed at which a person travels is expressed by y, and the speed at which a train travels is expressed by x. (x-y) 8=(x+y) 7 can be simplified, x=15y can be obtained; (2) When the train meets B 5 minutes later, the distance between A and B is: 5x-5y=5 15y-5y=70y; (3) The time it takes for A and B to meet is equal to the distance divided by the speed of both of them and 70y (y 2) = 35 minutes.