What are the specific types of fractional equation application problems, such as work efficiency cla

Fractional equationsThere are five common types of word problems:

1) Itinerary issues.

The basic formula: distance, speed, time, and the journey problem is divided into encounter problems.

Catch up on the problem. 2) Number problem: In the number problem, it is necessary to master the notation of decimal numbers.

3) The basic formula of engineering problems: workload, man-hours, and ergonomics.

4) Downstream and backward water problem v forward water v static water v water v reverse water v static water v water.

Steps:

Go to the denominator. Both sides of the equation are multiplied by the simplest common denominator at the same time, and the fractional equation is transformed into an integral equation. If you encounter numbers that are opposite to each other. Don't forget to change the symbols.

Lowest common denominator: The coefficient is the lowest common multiple.

The unknown number is taken to the highest power; Factors that appear.

take the highest power).

Transposition. Move items, if there are parentheses, you should remove the parentheses first, pay attention to changing the number, and merge similar items.

Convert the coefficient to 1 to find the value of the unknown.

Root inspection. After finding the value of the unknown, it is necessary to check the root, because in the process of converting the fractional equation into an integral equation, the range of the value of the unknown is expanded, and the root may be increased.

If the simplest common denominator is equal to 0, the root is an incremental root. Otherwise this root is the root of the original fractional equation. If the solved roots are all incremental roots, then there is no solution to the original equation.

The above content refers to: Encyclopedia - Fractional Equation.

Summary. There are six types of fractional equation application problems and formulas.

It takes X days for Team A to complete it alone, and Team A needs to complete the project separately.

If teams A and B cooperate for 3 days, the rest of the work will be completed as scheduled by team B alone" 3) x = 36 7

When 3 when 36 7It is better to use the (3) scheme when

Zhang Ming and Li Qiang participated in the 3000m Games, the speed ratio of Zhang Ming and Li Qiang was 5:6, and Li Qiang arrived 100 seconds earlier than Zhang Ming.

Solution: Let Zhang Ming's velocity of 5xm s and his velocity of 6xm s multiply 30x on both sides of the equation to obtain.

18000-3000x=15000

Solution: x=1

Test: When x=1, 30x≠0, x=1 is the solution of the original fractional equation.

5x=5 6x=6

Answer: Zhang Ming's speed is 5m s, and Li Qiang's speed is 6m s

23.(10 points) In the process of road reconstruction, a city needs to lay a pipeline with a length of 1,000 meters, and it is decided that two engineering teams A and B will complete the project. It is known that Project A can lay 20 metres more per day than Project B, and that the number of days it takes for Project A to lay 350 metres is the same as that for Team B to lay 250 metres.

1) How many meters can each of the A and B teams lay per day?

2) If the construction period for the completion of the project is required to be no more than 10 days, how many schemes are there for allocating the quantity (in 100 meters) to the two engineering teams? Please help me design it.

23.(1) Solution: If the first engineering team can lay rice every day, then the second engineering team can lay () meters every day.

According to the title:2 points.

Solution3 points.

Test: is the solution of the original fractional equation. 4 points.

Answer: Engineering teams A and B can lay rice and rice respectively every day. 5 points (2) solution: set the meter assigned to engineering team A, then assigned to engineering team B ( ) meter.

7 points are awarded for the solution of the question.

So there are 3 types of distribution schemes

Scheme 1: Allocate meters to project team A and project team B meters;

Scheme 2: Allocate meters to project team A and project team B;

Plan 3: Allocate 10 points to project team A and 10 points to project team B.

A wholesale and retail stationery store stipulates that anyone who buys more than 300 pencils at a time, (excluding 300 pencils), can pay at the wholesale price, and can only pay at the retail price for purchases of less than 300 pencils (including 300 pencils). Xiao Ming came to the store to buy pencils, if he bought 1 pencil for each 8th grade student, then he could only pay at the retail price, which cost 120 yuan, and if he bought 60 pencils, then he could pay at the wholesale price, which also cost 120 yuan, 1) What is the total number of students in this eighth grade?

2) If the purchase of 6 sticks at the wholesale price is the same as the purchase of 5 sticks at the retail price, how many 8th grade students are there in this school?

x+2) finger socks (x-2) = x (x+1) x+2) (x+1) = x(x-2).

x²+3x+2=x²-2x

x²+3x+2-x²+2x=0

5x+2=0

x=2/53x-5)/(x-1)-(2x-5)/(x-2)=13x-5)(x-2)-(2x-5)(x-1)=(x-5)(x-1)3x²-11x+10-2x²+7x-5=x²-6x+53x²-11x+10-2x²+7x-5-x²+6x-5=02x=0x=0

Solution: If the speed of the bicycle is xkm h, then the speed of the car is 3xkm h15 3x+40 60 15 x

5/x+2/3＝15/x

15+2x＝45

2x 30x 15 (km trapped h).

3x＝45（km/h）

The number of people in Class A is x.

4/5×250/x=192/x-2

8x=400

x = 50 per capita donation is 250 50 = 5 (books).

Class A donated 5 books per person, and the number of people was 50.

Solution: (1) It takes X days and Y days for two engineering teams A and B to complete separately.

According to the problem: x=y+30 (1 x+1 y)=1 20 x=60 y=30

2) Set up a and B cooperation to complete the project in y days.

1 60 * a + (1 20 + 1 30) y = 1 y = 60-3a (2) The first engineering team needs to be constructed for x days.