Travel Problem (1) Distance, time and speed are three basic quantities of travel problem, and their relationships are as follows: distance = time× speed, distance = time× speed, time = distance ÷ speed, time = distance ÷ speed, speed = distance ÷ time. Speed = distance/time. This lecture is to deepen the understanding of these three basic quantitative relations through examples. Example: 1 A motorcade slowly passed a 200-meter-long bridge at a speed of 4 meters per second, and it took * * * 1 15 seconds. It is known that each car is 5 meters long and the distance between two cars is 10 meter. Q: How many cars are there in this convoy? Analysis and solution: To find out how many cars there are in the fleet, we need to find out the length of the fleet first, which is equal to the analytical solution distance of the fleet115s minus the length of the bridge. "Distance = time × speed" means that the distance of motorcade 1 15 seconds is 4×115 = 460m). So the length of the motorcade is 460-200=260 (meters). From the problem of planting trees, it can be concluded that the motorcade has (260-5) ÷ (5+10)+1=18 (vehicles). Example 2 rides a bike from A to B at the speed of 10 km/h and arrives at 1 in the afternoon; Drive at the speed of 15km/h and arrive at 1 1 in the morning. What speed should I drive if I want to arrive at noon 12? Analysis and solution: There is no distance between A and B, that is to say, there is neither time nor distance, and there is no departure time for analyzing and solving this problem, so it seems impossible to find the speed. This requires finding out the time and distance through known conditions. Suppose A and B leave from A to B at the same time, A travels 10 km per hour and arrives1in the afternoon; B every hour 15km, and arrive at 1 1 in the morning. When B arrives at B, A is still 10×2=20 (km) away from B, which is the distance that B travels from A to B more than A. Because B has more 15- 10=5 (km) lines per hour than A, the time for B to travel from A to B is 20 \. So A and B start at 7 am, and the distance between A and B is 15×4=60 (km). If you want to arrive at noon 12, that is, if you want to drive 60 kilometers at (12-7=)5 o'clock, the speed should be 60 ÷ (12-7) =12 (km/h). Example 3 Two racing schemes were discussed before the rowing competition. The first scheme is to row halfway at the speed of 2.5 m/s and 3.5 m/s respectively; The second scheme is to arrange half the competition time at the speed of 2.5 m/s and 3.5 m/s respectively. Which of the two schemes is better? Analysis and solution: When the distance is fixed, the faster the speed, the shorter the time required. In these two schemes, the speed is not fixed, because it is not easy to directly compare the analysis and solution. In the second scheme, because the paddling time of the two speeds is the same, the paddling distance at the speed of 3.5m/s is longer than that at the speed of 2.5m/s .. The paddling distance at the speed of 2.5m/s is represented by a single line, and the paddling distance at the speed of 3.5m/s is represented by a double line, so a comparison diagram of the two schemes is drawn as shown in the following figure. Where section A+section B = section C. ..

In paragraphs A and C, the two schemes take the same time; In section B, because the distance is the same, and the second scheme is faster than the first scheme, the second scheme takes less time than the first scheme. To sum up, of the two schemes, the second scheme takes less time than the first scheme, that is, the second scheme is better. Example 4 Xiaoming climbs the mountain, walking 2.5 kilometers per hour when going up the mountain, walking 4 kilometers per hour when going down the mountain, and it takes 3.9 hours to go back and forth. Q: How many kilometers did Xiao Ming walk back and forth? Analysis and solution: Therefore, if we can find that we need to walk 1km up the mountain and 1km down the mountain, we need to analyze and solve the problem. Because the distance between going up and down the mountain is the same, we can find out the total distance between going up and down the mountain. Because it takes 1 km to go up and down the mountain.

So the total distance up and down the mountain is

In the travel problem, there is also a concept of average speed: average speed = total distance ÷ total time. Average speed = total distance/total time. Average speed For example, the average speed of going up and down the mountain in Example 4 is

An ant crawls along three sides of an equilateral triangle. If three sides crawl 50 cm, 20 cm and 40 cm per minute, how many centimeters do ants crawl per minute on average? Solution: Let the side length of an equilateral triangle be l cm, then the time required for an ant to crawl for one week is

Ants crawl once a minute on average for a week.

There is a kind of "drifting with the flow" in the travel problem. When we use the relationship between distance, time and speed to solve such problems, we should pay attention to the meaning and relationship of various speeds: downstream speed = still water speed+water speed, downstream speed = still water speed+water speed, countercurrent speed = still water speed-water speed, still water speed. Here, the still water speed, downstream speed and countercurrent speed refer to the speed of the ship in still water, downstream and countercurrent respectively. The distance between two wharves is 4 18km. Motorboat needs 65,438+065,438+0 to travel downstream and 65,438+09 to travel upstream. Find the velocity of the river. Solution: water velocity = (downstream velocity-countercurrent velocity) ÷ 2 = (418 ÷1-418 ÷19) ÷ 2 = (. Exercise 1 1. Xiaoyan goes to school by bike and walks home, which takes 50 minutes. If you walk back and forth, it takes 70 minutes. How long does it take to go back and forth by bike? 2. Someone wants to go to a farm 60 kilometers away. At first, he walked at a speed of 5 kilometers per hour. Later, a tractor with a speed of 18 km took him to the farm, which took 5.5 hours. Q: How far did he go? 3. It is known that the length of the railway bridge is 1 000m, and a train passes through the bridge. It is measured that it takes 1.20 seconds for the train to get off the bridge completely from the beginning, and the time for the whole train to stay on the bridge completely is 80 seconds. Find the speed and length of the train. 4. Xiaohong takes a break every 30 minutes when going up the mountain 10 minute, and takes a break every 30 minutes when going down the mountain for 5 minutes. It is known that Xiaohong's downhill speed is 0.5 times of 65438+ uphill speed. If it takes 3: 50, how long will it take to go downhill?

The car traveled from A to B at a speed of 72km/h, and immediately returned to A at a speed of 48km/h upon arrival. Find the average speed of the car. 6. The distance between the two places is 480 kilometers.