1, the formula of meeting problem: meeting distance = speed × meeting time. Meet time = meet distance ÷ speed and. Speed sum = meeting distance/meeting time.

For example, A and B walk in opposite directions at the same time from two places 120km away. The speed of A is 60 kilometers per hour, and the speed of B is 40 kilometers per hour. How many hours did they meet?

Solution: Suppose it takes X hours for two people to meet. According to the meaning of the question, we get (60+40)x= 120, and we get x= 1.2 hours.

A: 1.2 hours later, they met.

2. Formula of engineering problems: general formula: working efficiency × working time = total amount of work. Total amount of work ÷ working time = working efficiency. Total amount of work ÷ efficiency = working hours.

Assuming that the total workload is 1: 1÷ working time = a fraction of the total workload completed in unit time to solve the engineering problem; 1What is the score that can be completed per unit time = working time.

For example, for a project, it takes 65,438+00 days for Team A to do it alone, and 8 days for Team B to do it alone. If two teams cooperate, how many days can the project be completed?

Solution: Let two teams cooperate to complete the project within X days. According to the meaning of the question (110+1/8) x =1,solve x=4 days.

Two teams can finish the project in four days.

3. Profit and discount formula: after-tax interest = principal × interest rate× time ×( 1-20%).

For example, if the purchase price of a commodity is in 80 yuan and the profit of the merchant is 20%, what is the price of this commodity?

Solution: Let the price of this commodity be X yuan. According to the meaning of the question, x-80=80×20%, and x=96 yuan.

The price of this commodity is 96 yuan.

4. The catch-up problem formula: speed difference × catch-up time = catch-up distance. Catch-up distance/speed difference = catch-up time. Catch-up distance ÷ Catch-up time = speed difference.

For example, two cars A and B travel from A to B at the same time. Car A is 60 kilometers per hour, and car B is 40 kilometers per hour. After 3 hours, a car arrives at b, and b car is still 100 km away from b, what is the distance between a and b?

Solution: Let the distance between A and B be x kilometers. According to the meaning of the question, it is 3×60=x, and the solution is x= 180 km.

A: The distance between A and B is180km.

5. The formula of the downstream problem: downstream speed = still water speed+current speed. Velocity = still water velocity-water velocity.

For example, when a ship sails along the water, the speed is 12 km/h, and when sailing against the water, the speed is 6 km/h. Find the speed of the ship in still water.

Solution: According to downstream velocity = still water velocity+current velocity, we can get: 12=v+6, and the solution is v=6 (km/h).

Skills to solve application problems;

1, read the topic and understand the meaning of the topic: first, you need to read the topic carefully and make sure you understand all the information of the topic. Application problems usually provide some background information, conditions and problems to be solved. For more complex application problems, it may take some time to understand the nature and requirements of the problem.

2. Identify the known and unknown quantities: After understanding the meaning of the question, you need to identify the known and unknown quantities given in the question. These quantities are usually clearly given in the title. For example, if 5 yuan buys 3 kilograms of apples per kilogram, how much does he have to pay? 5 yuan in this issue is a known amount, 3 kilograms and how much money to pay are unknown.

3. Establish a mathematical model: After finding the known quantity and the unknown quantity, we need to establish a mathematical model to connect them. This model is usually an equation or set of equations describing the relationship between known quantities and unknown quantities. For example, in the application of the above Apple problem, we can establish the following equation: x=5×3, where x is an unknown number, representing the amount of money that Xiao Ming needs to pay.

4. Calculation: Use appropriate mathematical tools (such as paper and pencil, calculator or mathematical software) to solve the equation or equation and find the value of the unknown quantity.

5. Integral answer: After finding the value of the unknown quantity, integrate it into the answer. This may involve converting the results into appropriate units or giving some extra information to make the answer more complete.