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Seeking mathematical interest problems
On the 1. Expressway, a car with a length of 3.5 meters is driving at a speed of 45m/ s, and a large truck with a length of 16.5 meters ahead is driving in the same direction at a speed of 35 m/s. What is the overtaking time for the car to catch up with the big truck?

Let it take time t to get the equation.

16.5+3.5=(45-35) tons

The solution is t=2s.

2. The speed of someone walking is 6 kilometers per hour, and the speed of cycling is 18 kilometers per hour. He walked half way from A to B, the other half rode a bike, and then returned to A along the same road, half walked and the other half rode a bike. As a result, the time to come back was one and a third less than when he went. Find the distance between a and b.

Assume that the distance between Party A and Party B is s.

2s =(6+ 18)*[(s/2/6+s/2/ 18)-4/3]

s=48

Party A and Party B race on the 400m track, and Party B walks 80m every minute. The speed of Party A is 1, and the speed of Party B is 1. Now Party A is in front of Party B 100 meters. How long did they walk in the same direction before they met?

Solution: suppose two people meet in x minutes,

1 1/4 1= 1.25

The speed of A = 80× 1.25 = 100 m/min (m/min).

According to the topic: (100-80)X=400- 100.

20X=300

X= 15

4. A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which advance at a uniform speed. It is understood that they set off at 8 am at the same time. By morning 10, they were still 36 kilometers apart, and by noon 12, they were 36 kilometers apart. Find the distance between a and b.

Let the distance between a and b be x.

(x-36)/( 10-8)=(36+36)/( 12- 10)

x= 108

Open the pipe and pour water into the water tank, which will be full in 5 minutes. When it is full, pull out the plug at the bottom, so that the water in the water tank can flow out after 10 minutes. Once, open the pipe and pour the water into the water tank. After a few minutes, I found that the bottom plug was not plugged. Plug it quickly, and it will be filled with water in the same time. How long did it take to fill the tank?

Set x minutes of * * * notes.

x/5 - x/ 10 + x/5 = 1

x = 10/3

6. For Route A, it takes 12 for A to complete the journey, and 15 for B to complete the journey. The time ratio of A and B is (), and the speed ratio is ().

The time ratio is

12: 15=4:5

The speed ratio is

( 1÷ 12):( 1÷ 15)=5:4

7. Simplified ratio:

( 1)7.5:4=(7.5× 10):(4× 10)=75:40= 15:8

(2) 1 1/2: 1/5 = (3 × 10): ( 1 × 10) = 15: 2.

(3)0.48: 1.2=(0.48× 100):( 1.2× 100)=48: 120=2:5

(4)56:72=(56÷8):(72÷8)=7:9

8. Kobayashi took out pocket money, 50% bought snacks and 24% bought stationery. Spend less money on stationery than on snacks 15.6 yuan. How much did he take?

15.6 ÷ (50%-24%) = 60 yuan

9. The pricing of commodity A includes 20% profit, while the pricing of commodity B includes 40% profit. The sum of the prices of commodity A and commodity B is 480 yuan, and the price of commodity A is higher than that of commodity B. What are the costs of commodity A and commodity B in 60 yuan?

The price of a commodity is

(480+60) ÷ 2 = 270 yuan

The price of commodity b is

480-270 = 2 10 yuan

The cost of a commodity is

270 ÷ (1+20%) = 225 yuan.

The cost of commodity b is

210 ÷ (1+40%) =150 yuan.

There are 26 students in class 10.6 (2), including 17 students in math group and 14 students in composition group. Q: How many students participated in both the math and composition groups?

17+ 14-26 = 5 people.