Example 1
A and B start from a distance of 200 meters on a 400-meter circular track and run at a constant speed in the same direction. When A catches up with B for the third time, B runs 2000 meters. Q: How many times faster is A than B?Solution:a.1.2b.1.5
c.1.6d.2.0
According to "A and B set off from a distance of 200 meters on a 400-meter circular track", it can be seen that A catches up with B for the first time, and A runs 200 meters more than B.
Every time A catches up with B, A runs one more lap than B. After two times A catches up with B, A runs 400 more than B 2=800 (meters).
A runs a total of 200 + 800 = 1000 (meters) more than B.
According to "B ran 2000 meters", it can be seen that A ran 2000 + 1000 = 3000 (meters). If A and B have the same time, then the speed ratio and distance ratio are also the same, and it can be seen that the speed of A is 3000 2000 = 15 times.
So, choose option B.
Knowledge Points:
Speed = distance time.
Example 2
There is an asphalt road that needs to be paved, and the two construction teams A and B can be completed in 3 days together, while the construction team B alone needs to be paved in 5 days. If A and B cooperate to lay for 1 day, and the B construction team has other tasks, how many days does it take for A to complete the remaining tasks alone?Solution:a.4b.5
c.5.5d.6
According to "the two construction teams A and B can be completed in 3 days when they cooperate in laying, and it takes 5 days for B construction team to lay alone", the total amount of work that can be assigned is 15 (common multiples of 3 and 5).
The sum of the work efficiency of A and B is 15 3 = 5. B's work efficiency is 15 5=3, then A's work efficiency is 5-3=2.
According to "A and B cooperate to lay for 1 day", it can be seen that the workload of A and B for 1 day is 1 5 = 5.
The remaining workload is 15-5=10.
According to "the remaining tasks are completed by A alone", it can be seen that A alone needs 10 2 = 5 (days).
So, choose option B.
Example 3
If an organization plans to carry out activities in a square open space with a side length of 18 meters, it needs to plant a bunting every 2 meters on all four sides of the open space, and if the four corners of the open space need to be planted with bunting, then a total of () bunting is required.Solution:a.32b.36
c.44d.48
According to the idea that a square with a side length of 18 meters is planted with colored flags every 2 meters, it can be regarded as a closed figure tree planting.
According to the closed graphic tree planting formula, the number of flag-planting surfaces = total length spacing = 18 4 2 = 36 (surfaces).
So, choose option B.
Knowledge Points:
Closed figure tree planting formula (e.g. enclosed in a circle, ellipse): number of intervals = total length spacing; Number of trees = number of intervals.
Example 4
There is a village C in the middle of the road from village A to village B, village C is building a road, only one car can pass, two cars drive from village A to village B, the first car departs from village A at 8:15, the second car departs from village A at 9:45, the speed of the first car is 60 kilometers per hour, and the speed of the second car is 75 kilometers per hour. When the first car passed through the village of C for 2 hours, it was overtaken by the second car. Q: When the first car arrived at Cing Village, what was the distance between the two cars?Solution:a.90 km.
b.75 km.
c.60 km.
d.30 km.
Let the first car arrive at Cing Village in T hours.
According to "the first car departs from Village A at 8:15, and the second car departs from Village A at 9:45", it can be seen that the second car goes 1 less than the first car5 hours.
According to "the first car was overtaken by the second car after passing through the village of C for 2 hours", it can be seen that the distance of the first car is equal to the distance of the second car.
According to "the speed of the first car is 60 kilometers per hour, the speed of the second car is 75 kilometers per hour", the equation can be calculated: 60 (t+2) = 75 (t+2-1.).5), the solution is t=55。
When the first car arrived at C-village, the first car went 60 5 more than the second car5-75×（5.5-1.5) = 30 km, i.e. the distance between two cars is 30 km.
So, choose option D.
Example 5
Tickets for a scenic spot are 7% off in summer and 3% in winter, and children under 8 years old are free of charge, with 20 yuan for cars and 10 yuan for amusement facilities. Xiao Zhu took his 4-year-old son to the scenic spot once in summer and winter last year, and each time he accompanied the child to take the car once and let the child play with the amusement facilities once. If the two of them spend 50 more in the attraction in the summer than in the winter, the full price of the attraction ticket is:Solution:a.$100.
b.$90.
c.80 yuan.
d.60 yuan.
The full price of the ticket for the scenic spot is X yuan.
According to "the cost of two people in the scenic area in summer is 50 more than in winter", the equation can be listed: 07x+20×2+10=（0.3x+20 2+10) (1+50%), which gives x=100.
The full price of the ticket to the scenic spot is 100 yuan.
So, choose option A.