9 Math Olympiad problems, urgent! 20 Olympiad questions, and answers, quick!

1) The distance between port A and port B is 360 kilometers, and a ship sails from port A to port B for 15 hours to arrive at the river, and returns to port A from port B to port A, and sails against the water for 20 hours to arrive. With a sailing speed of 12 kilometers per hour, how many hours does it take to travel between the two ports?

Ship speed x current velocity y

360/15=x+y

360/20=x-y

x=21 y=3

360 (12+3) = 24 hours.

360 (12-3) = 40 hours.

A total of 20 + 40 = 64 hours.

2) A boat sails 20 kilometers per hour in still water, and in the river with a current speed of 4 kilometers per hour, it takes a common hour to travel to and from the two piers A and B, and find the distance between the two piers A and B.

s/（20+4） +s/（20-4）=

s = 1203) lay small squares of cement bricks with a side length of 50 cm around a square pool with a side length of 25 m. If three layers of cement bricks are laid next to the edge of the pool to become a three-layer hollow phalanx, how many cement bricks are supplied and supplied?

4) There is a road where team A takes 10 days to study alone, team B takes 12 days to study alone, and team C takes 15 days to study alone. Now let the three teams and repair, but the middle team A evacuated to another construction site, and the result was that the public took 6 days to complete the construction of the road. When Team A withdraws, how many days will it take for the Republic of B and C to be completed?

Let the total amount be 60: A 60 10 = 6 per day, B 60 per day 12 = 5, C per day = 60 15 = 4

If A does not leave, it can be completed in 6 days (6+5+4)*6=90

Illustrates that A has done less (90-60) 6 = 5 days.

That is, B and C and repair for 5 days.

5) The walking speed of A, B and C is 30 meters per minute, 40 meters per minute, and 50 meters per minute. A and B are in place A and C are in place B, and they are walking in the same direction at the same time, and C meets A 10 minutes after meeting B. Q: How many meters apart are abs?

Let ab=xx (50+30)-x (50+40)=10

x = 7200 meters.

6) A and B respectively from the two places of AB at the same time opposite each other, after 5 hours of meeting, after the encounter continued to move forward, after another 3 hours, car A arrived at place B, at this time car B is still 120 kilometers away from place A. What is the speed of A and B?

In 8 hours, A walks 120 kilometers more than B, so A walks 120 more than B per hour 8=15 kilometers.

Let B speed x A = x + 15 Total distance = 8 (x + 15) = 5 (x + x + 15).

x= A=7) The walking speed of A, B and C is 30 meters per minute, 40 meters per minute, and 50 meters per minute. A and B are in place A, and C sets off at the same time in place B to catch up with A and B, and C catches up with A and then catches up with B after 10 minutes. Finding ab distance?

b---a---c---d

Let ab=xx (50-40)-x (50-30)=10

x=200

I'm dizzy. Landlord, you use your own brain, don't always rely on the Internet to ask for help from others, this time develop a kind of dependence psychology!

Besides, you may not have listened to such a simple question in class, right?

1) Let the speed of the ship itself be v and the current velocity be u, then, v+u=360 15=24, v-u=360 20=18The solution yields v=21 and u=3. When downwind, the speed of the sailboat is 12 + 3 = 15 and the time is 360 15 = 24, and when the wind is upwind, the speed is 12-3 = 9 and the time is 360 9 = 40, which takes a total of 64 hours.

2) Let the distance between the two piers be x, when going downstream, the time t1=x (20+4), when going against the current, the time t2=x (20-4), t1+t2=, and the solution is x=120

3) What does it mean to shop three layers?

4) If the total project is 1, then A, B, and C can complete 15 per day, and B and C complete a total of 6 12 + 6 15 = 9 10 in 6 days, and leave 1 10, then A only worked for one day, so B and C and repair 5 days.

5) Let the time taken by B and C to meet is t, then (40+50)t=(30+50)(t+10), the solution is, t=80, ab is (40+50)t=7200.

The environment is a good place.

There is a batch of fruits, which can only be filled with a large basket of 8o, and can be filled with a small basket of 12o. It is known that each large basket carries 2o kilograms more than each small basket, so how many kilograms are there in this batch of fruit?

The answer is: seconds, meters, meters.

Seconds: 6The express train is 96 meters and the slow train is 72 meters.

7.The body is 80 meters long and has a speed of 13 meters per second.

8.The body is 300 meters long and 20 meters in seconds.

9.The car is 70 meters long and takes 15 seconds.

51 minutes, seconds, seconds.

53 minutes. 37 minutes.

seconds, meters, seconds. 20 minutes, seconds, kilometers, meters, seconds.

Step 1: According to the topic: Set a bottle of drink as x yuan, and a bottle of yogurt is (139 5x) Explanation: (139 5x) is the total price minus the price of the drink = the total price of yogurt, and if there are 6 bottles of yogurt, divide by 6 is the unit price of each bottle.

Step 2: Then there is the equation:

6x+(139－5x)÷

The solution is x=5, so the price of yogurt is: (139

5x) 6=19 (yuan).

The above is the first question.

Question 2. If the landlord has learned binary once, he should be.

2,000 seats means 2,000 tickets.

According to the title: there are x ordinary tickets and y VIP tickets.

then there is a system of equations.

x+y=2000

Solution: x=1400

y=600, there are 1400 regular tickets. There are 600 VIP tickets.

Explanation: General seat + noble seat = all seats.

The general seat money minus the money of the noble seat = 1100 yuan.

That's it. If it doesn't have a binary one.

It can be calculated according to the formula 4x+1100=(2000-x).

Landlord. I've been playing for 20 minutes. Give it points.

1.Let each bottle of beverage weigh x kilograms, and each bottle of yogurt weighs y kilograms

1) 5x+6y=139, (2)6x+5y=125g.

1)*6-(2)*5: 11y=209, y=19kg, x=72Set up VIP ticket friends x tickets, get:

4x+1100=(2000-x), solution:,x=600, so there are 600 VIP tickets for the theater and 1400 for ordinary tickets.

The reason is simple, some of the main diagonal lines overlap when he splices, although it is difficult to detect with the naked eye. You can calculate the slope of the same part of the two graphs. Since there is no diagram, it cannot give you a detailed calculation process, only an idea.

I remember it was the original question in the math textbook.

There is an auxiliary line that does not have the properties he is given.

If the total number of workers is added (supplemented) to 40 people, then the number of male workers is 3 times that of female workers.

Now the total number of people: 560 + 40 = 600 (people).

Number of female workers: 600 (3+1)=150 (person) Number of male workers: 150*3-40=410 (person).

The number of female workers is x

The number of male workers is 3x-40

x+(3x-40)=560

x = 150 then the number of women workers is 150.

The number of male workers is 3*150 40 410.

There are x number of male workers.

then there were 560-x women workers.

x=3×（560-x）-40

Male workers have. x = 410 people.

1 (1 15 + 1 10) = 6 hours.

8 workers and one belt conveyor do 1 to 15 per hour

5 workers and 3 belt conveyors do 1 to 10 per hour

So 13 workers and 4 belt conveyors do (1 15 + 1 10) per hour, so they need 1 (1 15 + 1 10) hours.

Solution: 13 people and 4 conveyors can be divided into two groups.

One group is 8 workers per conveyor.

The other group is 5 people with 3 conveyors

The speed of 8 people and one conveyor to transport this batch of goods is: 1 155 people and 3 conveyors to transport this batch of goods: 1 10, so it takes 1 (1 15 + 1 10) = 6 hours for two groups to transport this batch of goods together.

Solution: Pay attention to the following diagram of the relationship between the numbers:

Workers conveyor time.

It can be seen that 13 workers and 4 belt conveyors can complete the delivery of this batch of goods in an hour.

In the case of columnar calculations, it should be understood as follows:

Assuming that Xiaoyu has been walking until the class time, then walking 80 meters per minute will exceed the school 80 * 6 = 480 meters, walking 50 meters per minute will be less than the school 50 * 3 = 150 meters, the difference between 480 + 150 = 630 meters, this distance can be multiplied by the speed difference from Xiaoyu to the time from the start to the class, so that the time from Xiaoyu to the class is equal to 630 (80-50) = 21 minutes, and the distance is equal to 80 * (21-6), Or 50*(21+3)=1200, the total formula is (80*6+50*3) (80-50)=21 minutes, 50*(21+3)=1200 meters.

Set the distance to x meters. Since the bell time for class is the same, there are:

x/80+6=x/50-3。

So x=1200 meters.

Set Xiaoyu is still x minutes away from class:

80（x-6）=50(x+3)

Solution x=21

So distance = 80 (21-6) = 1200

Set the time to t minutes.

80（t-6）=50（t+3）

t = 21 distance is 80 (21-6) = 1200 meters.

Assuming x meters, then x 50-x 80 = 6 + 3, the solution is 1200 meters.

1.1 3 of A + 40% of B = both are 3 times larger.

120% of A + B =

A + B = where 120%-1 = 20% of B corresponds to hectares.

B = hectares. A = hectares.

1. Let X hectares in A and y hectares in B be obtained.

x+y=x/3+y*2/5=

The solution is x=, y=

2 Xiaohong has a total score in 4 tests, and a total of 370 + 100 = 470 points in five tests.

The average of the five times is 470 5 = 94 points.