Primary 6 Mathematics Olympiad Please answer in detail, thank you 28 17 1 19

Volume of water = 31 * 31 * 8 = 7688 cubic centimeters.

The cone stands upright in the container, and the height of the water rises to 12 cm, so the cone is not completely submerged, and the volume of the cone immersed in water at this time = 31 * 31 * (12-8) = 3844 cubic centimeters.

The volume of the cone in the part that is exposed to the surface of the water The volume of the entire cone.

The square of the height of the cone of the part that outcrops the surface of the water The square of the height of the entire cone.

So the volume of the cone of the part immersed in water The volume of the whole cone = 24 25 So the volume of the whole cone.

Cubic centimetre. cubic decimeters.

The cone stands upright in the container, and the height of the water rises to 10 cm, so the cone is not completely submerged, and the volume of the cone immersed in water at this time = 13 * 13 * (10-6) = 676 cubic centimeters.

The volume of the cone in the part that is exposed to the surface of the water The volume of the entire cone.

The cube of the height of the cone of the part that is exposed to the surface of the water The cube of the height of the entire cone.

So the volume of the cone of the part immersed in water The volume of the whole cone = 26 27 So the volume of the whole cone.

702 cubic centimeters.

The water part is a small cone, the height is 1 3 of the large cone, and the radius is 1 3 of the large cone, so the volume is 13*13*(10-6) divided by (1-1 3 to the third power) = 702

For cup C, don't consider the ones that are poured in, after the cup C is poured out 1 10, there are 9 liters left, then before pouring:

9 (101 10) = 10 liters.

That is, cup C poured into cup A is 10 liters of 1 10, that is, 1 liter.

Cup A accepts this 1 liter as 9 liters, and before acceptance it is 8 liters.

Cup A poured to Cup B 1 3, and there were 8 liters left, then there was originally:

8 (1-1 3) = 12 liters.

Then it poured a cup of 4 liters.

After pouring out 1 4 cups and leaving 9 liters, there is a "

9 (1-1 4) = 12 liters.

Remove the 4 litres poured from cup A to cup B, and cup B originally had 8 litres.

Cup B pours 3 litres for cup C (this is based on 12 litres).

Cup C received 3 liters, poured out 1 liter, and left 9 liters, so there were originally 7 liters.

A: 12; B: 8; C: 7.

The sum of the three is 27, which is exactly 9*3.

' A, B, C.

After three times 9 9 9

After the second 8 9 10

Once after 8 12 7

Once before 12 8 7

A 12 liters, B 8 liters, C 10 liters, hehe is very simple.

If you count it backwards, 9 (1-1, 10)=10, then C's 1 10=1, then A has (9-1) (1-1, 3)=12

B9 (1-1 4)=12 originally had 12-12*1 3=8

C originally had 9*3-12-8=7

The distance difference is 360-216 = 144 meters.

Time difference 24-16 = 8 seconds, speed = 144 8 = 18 m seconds.

The length of the car is 24 * 18-360 = 24 * (18-15) = 72 meters.

If you miss it, the speed of the two cars will be more than two seconds.

Time required (72+75) 42=seconds.

1) Set the length of the train to do the town ant x

360+x) Pure burial 24 = 216+x) 16x= (360x16-24x216) 8

v=(x+360) 24

2) (x+5)/

Conversion unit "1".

There are two sections of cloth, one section of cloth is 40 meters long, and the other section is 30 meters long, after using the same length of both sections of cloth, it is found that the remaining length of the short section of cloth is 5 7 of the remaining length of the long section of cloth, how many meters is used for each section of cloth?

40 30 10 meters.

10 2 7 35 meters.

40 35 5 meters.

Science and technology books are 3 4 of literary books, *** is 1 3 of the other three books, history books are 1 4 of the other three books, history books are 80 less than literature and art books, how many of the four books bought back?

80 4 35 = 20 * 35 = 700 copies.

The fruit store wholesaled four kinds of fruits, the weight of the pear is 4 5 of the apple, the weight of the orange is 6 25 of the other three fruits, the banana is 7 24 of the other three fruits, the banana is 120 kg less than the apple, how many kilograms of these four fruits are wholesaled?

Conversion unit "1".

120 3 31 = 1240 kg.

Concentration issues. There are 600 grams of brine with a concentration of 7%, how many grams of salt need to be added to increase the concentration of brine to 10%?

600 (1-7%) 558 (g).

588 (1-10%) 620 (g).

620-600 20 (g).

A: Add 20 grams of salt.

Pour 40 grams of brine from a 100 g cup full of 80% brine, fill the cup with fresh water, pour out another 40 grams of brine, and then fill the cup with fresh water, after repeating this three times, what is the concentration of brine in the cup?

100 80% 80 (g).

40 80% 32 (g).

80 32) 100 48% 40 48% g).

80 32 40 g).

Answer: After repeated three times, the concentration of salt water in the cup is.

1. A commodity is priced at 25% of the profit, and then it is discounted, and the number of pieces sold per day has doubled, so how many percent of the total profit of this commodity has increased every day compared with before the price reduction?

Answer: The total cost of the number of pieces sold per day before the price reduction is regarded as: "1", then the total profit obtained every day before the price reduction is 25%, and the total profit obtained every day after the price reduction is (1+, so the total profit of operating this commodity every day after the price reduction has increased compared with before the price reduction.

The two cities are 930 kilometers apart, and the passenger and freight cars drive out of the two cities at the same time, and after 6 hours the two cars meet The average passenger car travels 80 kilometers per hour, and the average truck travels how many kilometers per hour?

Solution: Set up trucks to travel an average of x kilometers per hour

80＋x）×6＝930

x 75A: The average truck travels 75 kilometers per hour

A and B two cars at the same time from the two stations of A and B, the two cars meet for the first time at a distance of 32 kilometers from station A, after the two cars continue to drive, after reaching each other at two stations A and B, they immediately return along the same road, and meet at 64 kilometers away from station A for the second time, how many kilometers are between the two stations A and B?

The time of the two encounters is fixed, so the distance traveled before and after the two encounters is also proportional. If A and B meet x full meters, car A will walk 32 kilometers and car B will walk 32 kilometers in the first encounter, and car B will walk in X-32 kilometers in the second encounter, and car A will walk X+ (X-64) kilometers and car B will walk X+64 kilometers. If there is 32 (x-32)=x+(x-64) x+64, then x is 80.

Human ergonomics and, for:

1 2 + 1 6 + 1 10 + 1 3 + 1 15) 2 = 7 12bcde4 artificial efficiency, is: 1 3 + 1 15 = 6 15 7 12 so a is water inlet, the work efficiency is: 7 12-6 15 = 11 60b is water inlet, and the work efficiency is:

1 2-11 60 = 19 60c for water discharge, the working efficiency is: 19 60-1 15 = 1 4d for water inlet, the working efficiency is: 1 6 + 1 4 = 5 12e for water discharge, and the working efficiency is:

5 12-1 3 = 1 12 The highest water injection efficiency is d, and the filling requirement: 1 5 12 = hours The highest water discharge efficiency is c, and the venting requirement: 1 1 4 = 4 hours 2

Take A and B as 1

It turns out that the speed ratio of Xiao Ming and Xiao Liang is 5:6

When they met for the first time, Xiao Ming traveled the whole process of 5 (5+6)=5 11, that is, the distance between the first encounter point and A was 5 11

When Xiao Liang arrived at A, Xiao Ming traveled the whole journey of 5 6, and the distance between Xiao Ming and B was 1-5 6 = 1 6

At this time, Xiao Liang speeds up, and the speed ratio between Xiao Ming and Xiao Liang is:

5:6 (1+1 4)=5:15 2=2:3 Xiao Ming finished the remaining 1 6, Xiao Liang did it again:

At this time, the distance between Xiao Ming and Xiao Liang is: 1-1 4 = 3 4 and then Xiao Ming also speeds up, and the speed ratio of Xiao Ming and Xiao Liang is:

2 (1+1 5):3=12 5:3=4:5 When the two met for the second time, Xiao Ming did it again:

The distance between the second encounter point and A is:

The distance between the two meeting points is:

The distance between A and B: 35 7 33 = 165 km.

1. Assuming that ABCDEs are all filled with water, the task of filling a pool of water is set to 1, and the corresponding water injection speeds are A, B, C, D, and E respectively

With the above information, the following equations can be listed:

2*（a+b）=1

6*（c+d）=1

10*（e+a）=1

3*（d+e）=1

15*（b+c）=1

Find this system of equations and get the following answer:

a=11 60 per hour.

b = 19 60 per hour.

c = -15 60 per hour.

d = 25 60 per hour.

e = -5 60 per hour.

The positive value is water injection, and the negative value is water release, that is: A needs 1 (11 60) = hours to fill the pool, B needs 1 (19 60) = hours to fill the pool, C takes 1 (15 60) = 4 hours to empty the pool, D takes 1 (25 60) = hours to fill the pool, and E takes 1 (5 60) = 12 hours;

The most efficient water injection is the D water pipe, which only takes hours; The most efficient way to discharge water is the C water pipe, which only takes 4 hours.

2. Solution: The distance ratio of Xiao Ming and Xiao Liang = speed ratio = 5:6

The first encounter is 5 11 from the ground of the first place

Xiao Ming arrived at place B and traveled the whole journey of 6 11

Then Xiao Liang traveled the whole course of 6 11 6 5 = 36 55

At this time, Xiaoliang is 36 55-5 11 = 1 5

The distance between the two is 1-1 5 = 4 5

In this case, the velocity ratio = 5 (1+20%): 6 = 1:1

Then the second place of encounter is 1 5 + 4 5 1 2 = 1 5 + 2 5 = 3 5

So the distance between A and B = 40 (3 5-5 11) = 40 (8 55) = 275 km.

I've done this before, you see.

Oh my God, what kind of topic is this, your child is amazing!

1.Let the total amount of water in a pool be 1, and the abcde is the efficiency of the abcde pipe (the inlet water is positive, the discharge water is negative).

a+b=1/2 c+d=1/6 e+a=1/10 d+e=1/3 b+c=1/15

The solution yields a=11 60 b=19 60 c=-1 4 d=5 12 e=-1 12

It is clear that d has the highest water injection efficiency and takes 1 (5 12) = hours c has the highest water discharge efficiency and takes 1 (1 4) = 4 hours.

2.We record Xiao Ming's starting point as A, and we need to calculate the distance between the first and second meeting points and A, and let A and B be separated by x kilometers. If the initial velocity of Xiao Liang is v, then the initial speed of Xiao Ming is 5 6*V, the return speed of Xiao Liang is 5 4*V, and the return speed of Xiao Ming is V.

The time required for the first encounter is x (5 6*v+v), and the distance between the first encounter point is x x (5 6*v+v)*5 6*v=5 11*x;

The second meeting point, that is, the distance run by Xiaoliang after changing speeds, can be divided into two parts: 1Xiao Ming before the speed change, 2After Xiao Ming shifts gear.

Before Xiao Ming changes speed: After the first encounter, Xiao Liang arrives at the end point first, at this time, Xiao Ming is still (x v)*5 6*v=5 6*x, and the remaining time before Xiao Ming's speed change is (x-5 6*x) (5 6*v), so the first part of Xiao Liang's distance is (x-5 6*x) (5 6*v)*(5 4*v)=1 4*x

After Xiao Ming changed the speed: The two ran a total of 3 4*x at the speed after the speed change, so Xiao Liang ran (3 4*x) (v+5 4*v)*(5 4*v)=5 12*xSo the distance of the second meeting point is a 1 4*x+5 12*x=2 3*x

2 3*x-5 11*x=35 so x=165km.

2.A and B are kilometers apart.

If the two places are separated by x kilometers, Xiao Liang's speed is a kilometer hour, then Xiao Ming's speed is 5 6a, the time taken by the two to meet for the first time is x (a+5 6a), and Xiao Ming's walking length is a*x (a+5 6a).

After the two increase their speed for the second time, Xiao Liang's speed is (1+1 4)a, Xiao Ming's speed is 5 6a*(1+1 5)=a, and the second time they meet, Xiao Ming's length from B is x (5 4a+a)*a, then a*x (a+5 6a)-x (5 4a+a)*a=35, then x=