Answer 22÷(6+5)=2 (hours)
Meet me in two hours.
Keys and skills to solve problems
This problem can be solved in two ways. (1) Find the sum of the speeds of two people per hour, and subtract the speed of A, which is equal to the speed of B. (2) Subtract the distance of two cities from the distance of Party A for two hours, which is equal to the distance of Party B for two hours. Find the dried rice that passes by every hour and divide it by 2.
Example 2 Two people, A and B, travel from two counties at the same time. A travels 6 kilometers per hour and B travels 5 kilometers per hour. They met two hours later. How far apart are these two counties?
Solution (6+5) × 2 = 22 (km)
The distance between the two counties is 22 kilometers.
Keys and skills to solve problems
Finding the distance between two counties is actually finding the sum of the distances between A and B, and the sum of the distances = the sum of the speeds × the meeting time.
The distance between the two counties is 22 kilometers. Party A and Party B set out from two cities at the same time and walked in opposite directions. Two hours later, they met. Party A walked 6 kilometers per hour, and how many kilometers did Party B walk per hour?
Solution (1): 22 ÷ 2-6 = 5 (km)
Method (2): (22-6× 2) ÷ 2 = 5km.
A: B travels five kilometers an hour.
Keys and skills to solve problems
The 22km in the title is the distance between two cities, the distance traveled by Party A and Party B, and actually the sum of their distances, while the (6+5) km traveled by Party A and Party B is the sum of speeds. Finding the "meeting time" means that the "sum of distance" includes several "sums of speed", that is, meeting for several hours.
Example 4 Two people, A and B, came out of two counties at the same time. A walks 6 kilometers per hour and B walks 5 kilometers per hour. After two hours, they are still 4 kilometers apart. How far apart are these two counties?
Solution (6+5) × 2+4 = 26 (km)
The distance between the two counties is 26 kilometers.
Keys and skills to solve problems
The whole process is divided into three sections: the section where A walked, the section where B walked and the section where B didn't walk. Add up these three paragraphs and get the distance between the two cities. So we can first find out 1 hour * * *, the distance that two people walk, that is, the sum of speeds, and then multiply it by the time that two people walk, so it becomes the sum of the two parts that have gone and have not. As shown in the figure below.
Example 5: A car and a bicycle leave from A and B at the same time. Four hours later, two cars met on the road. The distance between A and B is 240 kilometers, and the car runs at a speed of 45 kilometers per hour. How many kilometers does the bicycle travel per hour? (solved by equation and arithmetic)
Solution (1): Set the bicycle to travel x kilometers per hour.
4x+ 45×4=240
4x=240- 180
4x=60
x= 15
Method (2): (240-45× 4) ÷ 4 = 15 (km).
A: Bicycles travel every hour15km.
Keys and skills to solve problems
When the two cars meet, the whole journey is divided into two parts: car and bicycle, with a total length of 240 kilometers. It is more convenient to solve this problem with this equation. With the arithmetic solution, you can think like this: the whole journey-the distance traveled by the car = the distance traveled by the bicycle, and then divide it by the time traveled by the bicycle to get the speed.
The distance between east and west is 60 kilometers. A rides a bike and B walks. At the same time, they started from two places, walked towards each other and met in three hours. It is known that the speed of A is faster than that of B 10 km. What is the speed of two people per hour?
Disarmament: (60÷3+ 10)÷2= 15 (km)
B:15-10 = 5km.
A: A's speed is15km, and B's speed is 5km.
Keys and skills to solve problems
A is faster than B 10 km/h, which is the "speed difference" of two people, and 60÷3= 20 (km) is the "speed sum" of two people per hour. So the speed of two people per hour can be solved by the method of "sum and difference problem"
There are 7200 TV sets to be assembled in two workshops. The first workshop assembles 250 TV sets every day, and the second workshop assembles them for 5 days. The first seminar can be completed in 4 days. Now that the two workshops are started at the same time, how many days will it take to complete the task? How many units were installed in each group of the two workshops when the task was completed?
Solution 7200 ÷ (250+250× 4 ÷ 5)
=7200÷(250+200)
=7200÷450
= 16 (days)
The first workshop: 250× 16=4000 units.
The second workshop: 7200-4000=3200 (unit)
Answer: 16 days can complete the task. When the task was completed, 4000 units were assembled in the first workshop and 3200 units were assembled in the second workshop.
Keys and skills to solve problems
The key to solve this problem is to ask the number of units assembled in the second workshop every day. According to "the first workshop can complete the assembly capacity of the second workshop in four days", 250×4= 1000 (units) is not only the workload of the first workshop in four days, but also the workload of the second workshop in five days. So with 1000÷5, you can get the number of units assembled in the second workshop every day.
The circular track of the stadium is 400 meters long. Xiao Gang and Xiao Hua are on the same starting line of the track and start in opposite directions at the same time. Xiaogang runs 152 meters per minute, and Xiaohua runs 148 meters per minute. A few minutes later, they met for the third time.
X minutes later they met for the third time.
152x+ 148x=400×3
300x= 1200
x=4
A: They met for the third time after 4 minutes.
Keys and skills to solve problems
Two people are running on the circular road. At first, they are "reversing", and later they become "opposite", so it is actually a matter of meeting. When they met, they just walked around. The total length is 400 meters, so when they met for the third time, they ran (400×3) meters. Therefore, it can be solved according to the equation of "A journey +B journey = the whole journey" or by arithmetic.
That is: (1) 400× 3 ÷ (152+148) = 4 (minutes).
(2) 400 ÷ (152+148) × 3 = 4 (points)
Port A and Port B are 662 kilometers apart. At 9 o'clock in the morning, a speedboat named Hanshan sailed from Port A to Port B. At noon 12, another speedboat named Tianyuan sailed from Port B to Port A. At 16, the two boats met. Hanshan is 54 kilometers per hour, and Tianyuan is faster than Hanshan. (Solve in two ways)
Solve the problem that Hanshan sailed before Tianyuan speedboat;
12-9=3 (hours)
The time from Tianyuan to Hanshan;
16- 12=4 (hours)
Method (1): Tianyuan is kilometers faster than Hanshan;
(662-54×3)÷4-54-54=500÷4-54-54
= 125-54-54
=17km
Method (2): Make Tianyuan x kilometers faster than Hanshan every hour. The following is omitted.
Keys and skills to solve problems
The time in this question is changed to "time", so it is simple to convert time into time. The conversion method is: end time-start time = elapsed time.
Example 10 A rides a motorcycle and B rides a bike. At the same time, start from A and B, which are 126 km apart, and walk in opposite directions. Three hours later, 24 kilometers away from the two city centers, A and B met. What are the velocities of A and B?
Disarmament speed: (126 ÷ 2+24) ÷ 3 = 29 (km/h)
Speed of B: (126÷2-24)÷3= 13 (km/h)
A:A rides a motorcycle at a speed of 29 kilometers per hour, and B rides a bicycle at a speed of 13 kilometers per hour.
The fifth-grade students in a school gather in several lines. If each line has 10 students, there are 8 more. If there are 13 people in each row, there are 7 people in one row. How many lines are there? A * * *, how many people are there?
Each row has 13- 10=3 people, so the difference is: 8+7= 15 people.
Therefore, the number of rows =[8+7]/[ 13- 10]=5 rows.
1 * * * There are: 10*5+8=58 people.
Experimental primary school students go for a spring outing by car. If there are 60 people in each car, 15 people can't get on the car. If there are five more people in each car, there will be one more car. Q: How many cars and students are there?
Number of vehicles =[ 15+65]/5= 16
* * * Student: 60* 16+ 15=975.