1. The tortoise and the hare run a 10,000-meter race. The hare's speed is 5 times that of the tortoise. When they start together from the starting point, the tortoise keeps running and the hare reaches a certain point and starts to sleep. When the hare wakes up, the tortoise is already 5,000 meters ahead of the hare. The hare catches up, but when the tortoise reaches the finish line, the hare is still 100 meters behind. So how many meters did the tortoise run while the hare was sleeping?

2. The distance around the lake is 24 kilometers. Xiao Zhang and Xiao Wang started from a certain point on the lake at the same time and walked in the opposite direction. Xiao Wang walks at a speed of 4 kilometers/hour and rests for 5 minutes after every hour (1/12 hours). Xiao Zhang walks at a speed of 6 kilometers/hour and rests for 10 minutes after every 50 minutes (5/6 hours). /6 hours). How long did it take for the two of them to meet for the first time after they set off?

3.100 students wanted to go to the Children's Palace, 27 kilometers away from the school. There was only one car that could carry 25 people. In order for all the students to reach their destination as soon as possible, they decided to combine walking and taking a car. Method, it is known that the walking speed of students is 5 kilometers per hour and the car speed is 55 kilometers per hour. How much time is required to ensure that all students reach their destination as soon as possible? (The time taken to get on and off the bus is not included)

4. There are 4 children, each of whom happens to be 1 year older than the other, and the product of their ages is 1680. So, what are their ages? Years?

5.a.b.c is a prime number, c is a single digit, and a*b c=1993, find the value of a b c.

6. The displacement of a ship is 20,000 tons. The ship’s deadweight is 90,000,000 N (g=10 N/kg).

Question (1) How much cargo can it carry at most?

(2) When sailing in the river after being fully loaded, what is the volume of the ship immersed in the water?

7. On Sunday, the math teacher Teacher Xu went to the market to buy 5kg eggs with a basket (the basket weighed 0.25kg). When Teacher Xu picked up the weighed eggs in the basket, she found that the eggs were heavier than the 5kg eggs she used to buy. The number was much less, so he put the eggs into the basket and asked the stall owner to refund the money for 0.5kg of eggs. How did he know that the stall owner underweighted the eggs by about 0.5kg (accurate to 0.1kg)? Please write down the analysis process. What inspired you from this (please briefly describe it in 1 to 2 sentences)?

8. In a volume of one cubic meter, there are four kinds of balls with diameters of 0.06\\0.05\\0.04\\0.03 meters. It is required that each kind of ball must be added. What are the values ??of these four kinds of balls? What proportions are needed to maximize the filling density and minimize the gap?

9. As shown in the picture, part of both sides of corner A falls on the rectangular piece of paper, as shown in the picture EF and GH, please fill in the rectangle On the paper, design a plan that can measure angle A (just draw a picture), and write down the measurement results.

The picture is roughly like (a rectangular row is connected to two lengths and one is connected to one length and one width, all are slanted)

10. A job takes 10 days to do alone, B It takes 15 days to do it alone. If A does it alone for a few days, and then B takes over, it takes 12 days. How many days does A do it?

11. There are 25 students, and they have to pass We went on an autumn outing to the other side of the river. There was only one boat on the river, and only 5 people could sit on it at a time. How many times would it take for them all to cross the river?

12. Two mothers and two daughters went to the supermarket to buy chickens. When they came back, each of them had a chicken in each hand. How many chickens should they buy at least?

13. Mother White Rabbit dug up a basket of radishes, exactly 40. Brother Rabbit took 23, and Brother Rabbit took 17. Mother White Rabbit criticized Brother Rabbit, you know Brother Rabbit gave Rabbit How many brothers do they have? They both have the same number of radishes?

14. Xiao Ming and Xiao Hua took 80 sticks. If Xiao Ming gave 20 sticks to Xiao Hua, they would have the same number of sticks. Xiao Ming and Xiao Hua would each get 80 sticks. How many sticks did you get?

15. Two mothers and two daughters went to the supermarket to buy chickens. When they came back, each of them had a chicken in each hand. How many chickens should they buy at least?

16. Aunt Zhang in the kindergarten was about to wash the dishes. Teacher Wang asked her: "How many bowls were used at noon today?" Aunt Zhang said: "12 children eat, each uses one rice bowl, on average Two people use one vegetable bowl, and three people use one soup bowl. How many bowls does Aunt Zhang need to wash?

17. A and B process the same batch of parts respectively. When A is half done, B does 40 fewer reps than A. B accelerates and completes it after 7.5 hours. At this time, A still has 20 reps to complete. What is B’s speed after accelerating?

18. American Fun Mathematics Master Syme puts books on a double-layered bookshelf, with volumes 6, 7, 2, and 9 on the upper shelf and volumes 1, 3, 4, 5, and 8 on the lower shelf. This gives a fraction of 6729/13458, which is exactly equal to 2 1. How to place the book so that its scores are equal to 1/3, 1/4...1/9

19. The ratio of the money on A and B is 4: 3. Mom gave A and B 70 yuan each. At this time, the ratio of money between A and B was 7:4. How many yuan did A and B originally have?