A 6th grade math Olympiad problem solved with proportions!! I really can t do arithmetic .

Speed ratio: 1: (1 + 1 4) = 4: 5

Time ratio: 5:4

Speed ratio: 1: (1+1 3) = 3:4

Time ratio: 4:3

10 (4-3)x4=40 (minutes).

The distance between A and B: 1x120=120 (km).

From:", if you increase the speed by 1 4, then you can reach it in 24 minutes longer than the time on the spot".

Now the speed is 1 + 1 4 = 5 4 Because the speed is inversely proportional to the time, the current travel time is 4 5 of the original travel time So the current time is 1-4 5 = 1 5 less than the original time Combined: "24 minutes to arrive" can get less 24 minutes is 1 5 of the original time So: the original time of the full length of the line is:

24 (1 5) = 120 minutes.

In the same way, according to the following "If you drive 80km at the original speed and then increase the speed by 1 3, then you can arrive at place B ten minutes in advance", it is concluded that after driving 80km, the original time for the remaining distance is:

10 (1 4) = 40 minutes.

So the time it takes to travel 80 kilometers at the original speed is: 120-40 = 80 minutes.

The original speed is: 80 80 = 1 km min.

The distance between A and B is: 120*1=120 kilometers.

1.Let A have x yuan and B have y yuan, then there is.

x/y=3/1

x-6)/(y+6)=2/1

x=54,y=18

2.Let A have a coincidence x book, B has a y book, and C has z book, then.

x+y+z=108

y-x=18

y/z=5/4

x=27,y=45,z=36

Person. 6.Let the number of pencil branches be x and the number of fountain pen branches be y, then.

x/y=5/4

y-36)/2=x/7

x=80,y=56

7.A is x, B is y, and C is z, then.

x+y+z=26

x/z=1/3

y/z=2/7

x=91/17,y=78/17,z=273/178.Let A have x people and B have y people, then.

x/y=7/3

x-30) filial piety source y=3 2

x=84,y=36

To use the formula for summing proportional sequences.

If the total number of people is x, the admission score is y.

1/3x*(y+6）+2/3x*(y-24)=60x

Don't ask how much time is tight.

13.Solution: Set the admission score line as x, and regard the total number of candidates as 1

6+x)*1 3+(x-24)*2 3=60x, x=74

A: The cut-off score for admission is 74 points.

15.Solution: Let the side of the square be x, then:

8+x)*(2+x) 2=2x 2+x 2+8x 2 Solution's Trembling Chakra, x=4

s abc is: (8+4)*(2+4) 2=36(cm2).

Too much, point to time.

I'm only in the fourth grade.

Solution: Suppose this batch of coal was actually burned for x days (x=

x=42

Let's say this batch of coal actually burned for x days.

The solution is x=42 (days).

Push back ---

After catching up with car B, he immediately returned to the system, and after arriving at place A, Bai immediately went to chase car A, and caught up with car A for the second time at a distance of 16,000 meters from dua. --

From this, it can be seen that car B DAO is three times the speed of car A, because car B travels three times the distance of car A in the same amount of time.

-8 minutes later, car B also departed from place A and caught up with car A at a distance of 8,000 meters from place A. --Car B takes two-thirds less time than car A in the same distance, and these 8 minutes are two-thirds of the time, so it takes only 4 minutes for car B in 8,000 meters.

As a result, car B ran a total of 4 8000 meters and took a total of 16 minutes, so it is now 9 hours + 16 minutes + 8 minutes = 9 hours 24 minutes.

a 8000 c 8000 d b

According to the title: it can be known: line segment ac 8000; cd＝8000；

When B is in point C for one time.

After getting on the first grade, he returned to A and then to D point to catch up with A for the second time, and he walked a total of 8000*3 24000 meters;

A took the same amount of time from point C to point D as B, but only walked 8,000 meters, which can be obtained:

B speed 3 times the speed of A.

According to the inscription: At 9:08, A has traveled 8 * A speed, and B begins to pursue;

Its pursuit time (8*A) (B, A) 4 minutes;

Thus finding B velocity 8000 4=2000 m min; That is: the time at point C is 9:12 a.m.;

When B pursued A for the second time, he traveled a total of 24,000 meters, which took 12 minutes, that is, from point C back to point A and then to point D, altogether.

It took 12 minutes, so the time for D o'clock is: 9:24 minutes.

That's it.

9:24 a.m.

Draw a line to see how good the diagram is.

Car B is leaving. 8000 meters after catching up with the car after the DAO: A inward.

After going 8,000 meters, B turned back to A and walked 8,000 meters, and chased 16,000 meters to catch up with car A for the second time. The distance ratio of A and B is the speed ratio: 8000: (8000 + 16000) = 1:3.

Let's look at the situation of the first chase: I walked for 8 minutes on the second night, and I walked 8,000 meters. The time ratio of A and B is the inverse ratio of velocity: 3:1. 8 minutes late is (3-1) servings. The 3 parts of the first walk are 12 minutes.

A walked another 8,000 meters and walked for another 12 minutes. That's 9:24.

Solution: The column formula is: 8+8 2 4=8+16=24 minutes, so it is 9.24 minutes.

The method is as follows: according to the title, when B catches up with car A for the second time, A travels two genera of 8000 meters, when catching up with A for the first time, car B takes the time of driving 8000 meters + 8 minutes, after catching up to catching up with A for the second time, B travels 3 8000 meters, and the time is the time of driving 3 8000 meters, and A travels two 8000 meters in the whole process, that is, The time taken by B to catch up with car A for the first time is the same as the time taken for car A to catch up with car A for the second time, therefore, car B traveled two 8000 meters in 8 minutes, so the column formula is: 8 + 8 2 4 = 8 + 16 = 24 minutes, so it is 9:24 at this time.

1. This batch of coal can be burned for x more days.

105：90=x：30

x=352, it takes x days to complete.

200-40) ：20 = 200： xx= 25

3. Repair x days to complete the task.

360：(360+40)=x：(30-10)x=18

1.Actual number of days = 105 30 90 = 35 days 2Daily = (200-40) 20 = 8 units.

Advance = 30-200 8 = 5 days.

3.Also = (360 30-360 10) (360 + 40) = 18 days.

The first will not (* hee-hee......

2.Let's say it takes x days to complete.

200-40) :20 = 200: xx= 25

3.Repair for x days to complete the task.

360:(360+40)=x:(30-10)x=18

I hope you will adopt my answer.

6 years old to learn the equation? I have taught elementary school students math application problems, sometimes it is a headache, the equation comes out at once, but it can't be used, and I and the child's parents just can't get it out, and they are all graduates of famous universities, hehe, don't tell me that I want to spend a line, and then find out the rules of calculation in the upper sections......

seconds to catch up with the drifting bottle;

Yuan Tai 3

Set the water flow speed a, the ship speed b, within 40 seconds, the bottle moves 40a downstream, the boat moves 40 (b-a) upstream, the distance between the U-turn is 40a + 40 (b-a) = 40b, the bottle speed after the U-turn is still a, the ship speed (b + a), and the ship relative to the bottle speed b, catch up with 40b b = 40

The product of the inner term is equal to the product of the outer term which is used in the proportional formula. 4a is equal to 5b, which can be converted to 4a 5b is equal to 1, 4 5 and multiplied by a b equals 1, then a b is equal to 5 4

[2-(one and a third and one and five twelveths] (two and two-thirds).

2-(one and a third and five fifteen and twelve, five twelve)] two and two-thirds).

The rest is easy, but too hard to fight.