Help, ask everyone two Olympiad questions, please help answer one Olympiad question

1. It takes X hours for A to complete this draft, then: 9 x + (1 x + 1 30) * 4 = 1 is to see the task as a whole 1, a matter of speed.

From the above equation: x=15, then B completes 1 10 of this manuscript per hour, so it takes 15 hours for A to complete alone, and 10 hours for B to complete alone.

2. Because s=vt, then time t=s v

From the question: s=10 9v*(s v-1 3)s=4 3v*[(s-72) v-1 2]+72 Because the unit of speed v is kilometers per hour, it is necessary to pay attention to the minutes into hours and then calculate.

S is found from the above two equations

If it takes x hours to complete, then A completes 1 x per hour of this manuscript and B completes 1 x + 1 30 of this manuscript per hour

9/x+4/x+4/30=1

The solution is x=15

And 1 x + 1 30 = 1 10

So A takes 15 hours and B takes 10 hours.

Set the travel x km, the original speed y km hour.

x/(10y/9)+20/60=x/y

72 y+(x-72) (4y 3)+30 60=x y, which gives x=540 7

1 Set: The speed of A and B is X A x B and the total manuscript Z

4 (x A + x B) + 5 x A = z

x B = z 30 + x A.

The solution is z x A = 15 z x B = 10

2 set: speed x time t total distance z

xt=zx(1+1/9)(t-20)=z

x(1+1 3)(t-30-72 x)=z-72 gives z=180

1-1 30*4) (4+4+5)=2 30, the velocity of A.

2 30 + 1 30 = 3 30, the speed of B.

s/x=ts/(10/9*x)=t-20

s-72) (4 3*x)=t-30+72 x to get s<0. I don't know if there is a mistake, the idea should be fine, you can confirm the topic again

The circumference of the semicircle is 63 cm. If the ants do not turn around and walk, use 63 (s i.e. meet due to 13 11 9 7 5 3 1 7, so after 13 11 9 7 5 3 1 49 seconds, the two ants meet.

Analysis: Actually, it's nothing.

1 3 5 7 9 11 13 You will regard the opposite as a positive number.

Facing away is considered negative.

You can get 1+3+5+7+9+11+13=49

[1 + (5-3) + (9-7) + (13-11) = 7, so the shared time is: 1 + 3 + 5 + 7 + 9 + 11 + 13 = 7 = 49 (seconds).]

（1）1/1o=1/12+1/60

2) Add 2 to the total number of people to be divisible, the smallest is 315, but it is not an even number, so take 2 times 630 of 315 and subtract 2.

Capacity: 628 people.

3）2450=49×50。Therefore, the total number of pages is 98 pages, and the sum of the first page plus the last page is the same as the sum of 49 + 50, so that the sum of each group of two pages is 99, and there are a total of 98 2 = 49 groups, so the total number is 99 49 = 4851

1/1o=1/12+1/60

Adding the total number of people by 2 happens to be divisible by du, the smallest is 315, but this zhi

is not an even number, so take 2 times of dao315 back to 630, and subtract 2 to 628 people) Answer: 2450 = 49 50.

The sum of the first page plus the last page is the same as the sum of 49 + 50, so that the sum of each group of two pages is 99, and there are a total of 98 2 = 49 groups, so the total number is 99 49 = 4851

In Equation 1 10 = 1 ( ) + 1 ().

In bai, two different natural numbers within () can be du (12) and (60).

The total number of people in the fifth grade of a certain elementary school is dao

A three-digit even number, minus 3 from the total number of people is divisible by five, minus five is divisible by seven, and subtracted seven is divisible by nine, then there are (628) people in the fifth grade of the primary school.

Each page of a book except the front and back covers is marked with page numbers on both sides, and if the product of the page numbers on both sides of a page is 2450, then the sum of all the page numbers of the book is (4851).

A better than a first to take 4 grains.

At this time, 2000 grains are won, and it is the turn of B to take it.

No matter how many grains B takes, A can take the corresponding number of grains, so that the sum of the number of grains taken by A and the number of grains taken by B is 8 (e.g. B takes 3 grains, A takes 5 grains, etc.).

After taking one round in this way, there are 1992 grains left, which can also be divisible by 8, and so on, when 249 rounds have passed, there are 8 grains left, and it is the turn of B to take it.

At this time, no matter how many pieces B takes, A can take the remaining pieces, so in the end, A wins.

B can win, A can never win.

1。The total number of chess pieces 2004 is an even number, A takes the first according to the rules, regardless of any odd number in any of the prescribed 1, 3, 5, 7, the remaining numbers are odd numbers, and A can never take the last one;

2。Because B is taken later, and according to the rules, after taking can always make the remainder an even number, no matter how clever A takes, B will always be able to wait for the opportunity to take the last grain, so B wins!

A takes 1 for the first time, then if B takes 1, A takes 7, if B 3, then A 5, B 5, B 3, B 7, A 1. In this way, each time it is reduced by 8, 250 after which there is 2004-1-2000 = 3, A takes 3, A wins.

1 3 5 7 9 The number of the nth item of the formula is 2n-1 The number of the first term is 1

From the first elephant to the nth item, we can see which one exceeds 2004 and the public test is (a1+an)*n 2 substituting [1+(2n-1)]*n 2=2004

Get n squared = 2004 n = so when n is 44, that is, when B takes it, it is 1996

When n is 45, that is, when it comes to A, it will exceed 2004, so A-wins.

1. Bucket B left: (150-120) (4-1) = 10 (kg) Bucket A remaining: 10 4=40 (kg).

Shared go: (120-10) 2 = 220 (kg) B warehouse: (940-40) (4-1) = 300 (kg) A warehouse: (300-40) + 940 = 1200 (kg).

120-y multiplied by four = 150-y

480-4y=150-y

3y=330

y=110A: Share 220 kg of oil.

1 question 150-x=4 (120-x), x=110, large 40, small 10, total 220

2. Set the position as x, the position A as 4x, 4x-940=x-40, x=300, 4x=1200

1.Group A 6 people, each person is 152-140 = 12 times less than the average, 6 people are 6 times less than the average, a total of 6 people are 6 * 12 = 72 times.

Group B had 160-152 more reps per person than the average = 8 times.

So Group B needs to have 72 8 = 9 people.

2.(12*5+10*3) (5+3)=RMB.

1. If there are students x in group B, then there are: 140x6+160x=152(x+6), and the equation can be solved to obtain x=9

2、（12x5+10x3）/8=

There are x students in Group B.

140*6+160x)=152(x+6)x=92 should be bought x yuan.

12*5+10*3=(5+3)*xx=

Because ab=10, ac=20, the length of the right-angled edge is half the length of the hypotenuse, so the inside angle corresponding to ab is 30 degrees.

That is, the angle c1ab1 = 30 degrees.

So the arc length from c to c1 is 150 degrees, and the radius is ac=20.

The length is: 150 360 * 2 * 20 = 157 3 = the arc length of the second segment is ab = 10 as the radius, the arc length of 90 degrees, and the length is:

So the distance traveled is =

First turn 150° with AC as the radius, and then turn 90° with BC as the radius, and calculate the addition of arc lengths.

The route from C to C1 is based on an arc length of 150 degrees with A as the center and AC as the radius, and the route from C1 to C2 is an arc length with B1 as the center, B1C1 is the radius and a central angle of 90 degrees.

150 20 180 + 90 10 180 = 65 3 cm.