Mathematics is the key to science. The following is the explanation material of the sixth grade math distance application problem I compiled. Let's have a look.

Examples of application problems in Grade 1 and Grade 6: Example 1: 1 A puppy found 1 running rabbits 8 meters in front of it and immediately caught up with them. It is known that the distance that a puppy runs two steps is equal to the distance that a rabbit runs five steps, but the rabbit runs fast, and the puppy can only run three steps when the rabbit runs five steps. How many meters does the puppy have to run to catch up with the rabbit?

Solution: Speed = distance? time

According to the relationship given by the topic:

The pace of two dogs = the pace of five rabbits (1)

3 Dog Walking Time =5 Rabbit Walking Time (2)

And dog steps? Dog walking time = dog speed

Rabbit pace? Rabbit walking time = rabbit speed

So: (1) formula? (2) Formulas are available

2 speed of dog =3 speed of rabbit.

That is to say, at a certain moment, the dog ran 3 meters and the rabbit ran 2 meters, with a difference of1m.

In order to make them 8 meters apart,

Then the dog runs for 24m and the rabbit runs 16m.

The puppy can run at least 24 meters to catch up with the rabbit.

Example 2: The speed of a car is 6 kilometers faster than that of a van. Cars and trucks leave school at the same time and drive along the same route. The car arrived at the city gate 10 minutes earlier than the van. When the van arrives at the city gate, it is 9 kilometers away from the city gate. How far is it from the school to the city gate?

Solution: First, calculate how long it takes from the school to the van to reach the city gate.

At this time, the car walked 9 kilometers more than the van, and the speed difference between the car and the van was 6 kilometers per hour. Therefore,

Time consumption =9? 6= 1.5 (hour).

The car arrived at the city gate 10 minutes earlier than the van. When the van arrived, it was 9 kilometers away from the city gate, indicating that the speed was 9? (10/60)=54 (km/h)

The van speed is 54-6=48 (km/h).

The distance between the gate and the school is

48? 1.5=72 (km).

A: The distance from the school to the city gate is 72 kilometers.

It takes 36 minutes for Xiao Zhang to walk from A to B, and it takes 12 minutes for Xiao Wang to ride a bike from B. They set out at the same time and met in a few minutes.

Solution: It takes Xiao Zhang 36 to walk the same distance. 12=3 (times), so the speed of cycling is three times that of walking. In other words, at the same time, Xiao Wang rode three times as far as Xiao Zhang. If the distance between A and B is divided into four equal parts, Xiao Wang takes three sections and Xiao Zhang takes 1 section. What time does Xiao Zhang spend?

36? (3+ 1)=9 (minutes).

A: The two will meet in 9 minutes.

Long-distance application exercise in grade two and six: 1. Jingjing walks to school every morning. If she walks 60 meters per minute, she will be five minutes late. If she walks 75 meters per minute, she can get to school two minutes earlier. How does Jingjing walk to school?

2. Party A, Party B and Party C walk together. Party A walks 60 meters per minute, Party B walks 67.5 meters per minute and Party C walks 75 meters per minute. Party A and Party B go from Dongzhen to Xizhen, and Party C goes from Xizhen to Dongzhen. Three people start at the same time. After meeting Party B, they will meet Party A in two minutes. What is the distance between the two towns?

3. Two cars, A and B, leave from Station A and bilibili at the same time. The two cars met for the first time at a distance of 32 kilometers from station A, and then continued to drive. After arriving at bilibili and Station A, immediately return along the original road and meet again at a distance of 64 kilometers from Station A. What is the distance between Station A and bilibili?

4. On the circular runway with a circumference of 400 meters, there are two points, A and B, which are 100 meters apart. A and B run back to each other at the same time. After they meet, B turns and A runs in the same direction. When A runs to A, B just runs to B. If A and B run at the same speed and direction in the future, then when A catches up with B, B will.

5. Lao Wang rode a bicycle from city A to city B on business, riding 15km per hour, and riding a motorcycle when he came back, which took him 33km per hour, which was 1.8h less than riding a bicycle, so as to calculate the distance from city A to city B..

6. Three fast, medium and slow trains started from the same place at the same time and caught up with the cyclist in front along the same highway. The three cars caught up with the cyclist in 6 minutes, 10 minutes and 12 minutes respectively. Now we know that the express train is 24 kilometers per hour and the medium-speed train is 20 kilometers per hour. How many kilometers does the local train travel per hour?

7. On the circular track, when two people run clockwise, they meet every 12 minutes. If the speed of two people is the same, one of them will run counterclockwise and meet every 4 minutes. How many minutes does it take for each person to run once?

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