1, normalization problem: If the engineering team plans to build a 4,800-meter-long road with 60 people in five days, in fact, 20 people are added, and each person will build 4 meters more than planned every day. How many days did it take to actually complete this road?
2. Encounter problems: For example, two cars, A and B, start from the east and west at the same time. The speed of A car is 56 kilometers per hour and that of B car is 48 kilometers per hour.
3. Catch-up problem: If the bus and the car leave in the same place and in the same direction, the bus travels 60 kilometers per hour and the car travels 84 kilometers per hour. The bus leaves two hours after the bus leaves, and the bus catches up with the bus a few hours later.
4. Crossing the bridge: If the train crosses a 2700-meter-long bridge, it takes 3 minutes to get on the bridge from the front and get off the bridge from the back.
5. Wrong train problem: For example, a passenger train is 280 meters long and a freight train is 200 meters long, and they are facing each other on parallel tracks. It takes 20 seconds from the two ends meeting to the tail separating. If two cars are driving in the same direction, with the truck in front and the bus behind, the time from the moment when the front of the bus meets the rear of the truck to the moment when the rear of the bus leaves the front of the truck is 120 seconds.
6. Navigation problem: If the passenger ship and cargo ship leave from Port A and Port B at the same time, the passenger ship and cargo ship will meet in 6 hours, but there is still 6 kilometers from the midpoint of the two ports.
The purpose of mathematics competition
Stimulate students' interest and love in mathematics: Let students feel the charm and challenge of mathematics by contacting higher-level mathematics problems, so as to enhance their interest and love in mathematics.
Improve students' mathematics literacy and ability: The problems in mathematics competitions are usually more challenging than those in daily classes. Students need to improve their mathematical literacy and problem-solving ability through continuous thinking and practice.
Cultivate students' logical thinking ability and innovative ability: Problems in mathematics competitions often need students to use logical thinking and innovative thinking to solve, and such training is helpful to cultivate students' logical thinking ability and innovative ability.