Elementary 1 Math Equation Application Problems Engineering Problems

Set the number of people to x, each person mowing grass per day for 1 unit, the area of small grassland y, then the area of large grassland 2y, mowing large grassland in the morning x*1 2=x 2;

In the afternoon, mow the large grass (x 2) * (1 2) = x 4;

Afternoon mowing small grass (x 2) * (1 2) = x 4;

The next day, the small grass is mowed by one person for one day, which is 1*1=1;

Then: x 2+x 4=2y

x/4+1=y

The solution is x=8, which means that the total number of lawn mowers is 8.

Analyse; Set: There are x number of lawnmowers in this group.

The solution to this problem is "the big meadow is twice as big as the small meadow".

Big Meadow: In the morning it was all (1 x) who worked for half a day (that is;

And in the afternoon it was half of the people (who worked for half a day (, that is. So it's time to get a big meadow.

small meadows; Half of the people (who worked for an afternoon (, that is.

On the 2nd day, it took another person (1) to work for one day (1), and it was 1. So get a small meadow rule;

Solution: x=8

So there were 8 people.

Solution: Let the total number of people be x, the work efficiency of each person is v, and the working time of half a day is tFrom the meaning of the title:

xvt+1 2xvt=2*(1 2xvt+2tv) to obtain x=8

A: There are 8 people in this group.

1. It is known that A and B cooperate in a project, A will complete it in 25 days alone, B will do it alone in 20 days, and A and B will cooperate for 5 days.

A has another task, and B will do it alone for a few more days?

Analyze and set B to do it alone for x days.

From the inscription, it can be seen that the ergonomics of A is 1 25, and the ergonomics of B is 1 20

1/20×x=1-（1/25+1/20）×5

Solution x=11

2. It takes 40 hours to organize a batch of books by one person. Now it is planned that some people will do it for 4 hours first, and then add 2 people to do it with them for 8 hours to complete the work. Let's say how productive these people are.

How many people should be assigned to work first?

Analyze and set up x people to work first.

From the question design, it can be seen that a person's ergonomics is 1 40, 1 40 (4+8)x+1 40 2 8=1

Solution x=23, a middle school student tidy up the playground by himself, if the first junior high school student is asked to work alone, it needs to be completed in hours, and if the second junior high school student is asked to work alone, it takes 5 hours to complete. If you let the beginning.

1. How much time does it take for the second year students to work together for 1 hour, and then the second year students to complete the rest alone?

The analysis and design took a total of x hours to complete.

From the question setting, it can be seen that the ergonomics of the first year of junior high school students is 1

The ergonomics of students in the second year of junior high school is 1 5

1/5 ×x+1/

The solution is x=13 3

4. It takes 80 hours to complete a batch of data by one person, and now it is planned to be done by some people for 2 hours, and 5 people will be added to do 8 hours, and 3 4 to complete this work, how to arrange the specific number of people involved in sorting out the data?

Analysis and pre-planning are done by x people.

As can be seen from the inscription, the ergonomics of a person is 1 80

1/80×（2+8）×x+1/80×5×8=3/4

Solution x=25, a pool armor, B, C three water pipes, a single pipe A can be filled in 10 hours, a single pipe B can be filled in 15 hours, and a single C pipe can be filled in 20 hours. Now the three-pronged pipe is opened, and the first pipe is closed halfway, and the result is that the wild imitation ride fills the pool in 6 hours, and asks how many hours has the first pipe actually opened?

The analysis and the ergonomics of pipe A are 1 10, the ergonomics of pipe B are 1 15, and the ergonomics of pipe C is 1 20

The armor pipe was actually opened for x hours.

Then 1 10 (6-x) = (1 10+1 15+1 20) 6-1

The solution is x=36, two candles of the same length, the coarse candle can be burned for 4 hours, the thin candle can be burned for 3 hours, a power outage, two candles are lit at the same time, the call is blown out at the same time, and it is found that the length of the coarse candle is twice that of the thin candle, and the power outage time is found.

Analyze and set the power outage time to x hours.

Coarse candles burn 1 4 = 3 12 per hour, and thin candles burn 1 3 = 4 12 per hour

1-1/4×x=（1-1/3×x）×2

Solution x = In short, solving engineering problems, treating the entire project as unit 1, and taking the reciprocal of time as the work efficiency is the key to solving the problem!

The area of the walls that need to be painted in each room is x

8x-40)/3=9x/5+30

Solution x=50

The area of the walls that need to be painted in each room is 50

The master brushes (8*50-40) 3=120 and the apprentice brushes 90 per day, and it takes Y days.

120+90*2）*y=36*50

y=6 takes 6 days to finish.

Master M people Apprentice n people.

36*50/3=600=120m+90n

20=4m+3n n=(20-4m)/385m+65n=z=85m+65(20-4n)/3=（1300-5m）/3

m=2 n=4

1.Each room is set in square meters.

8x-40/3 - 9x/5=30

40x-200-27x/15=30

13x-200=450

x = 50 square meters 8x-40 3 = 120

9x/5*2=180 1800/300

Let the wall area to be painted in each room be x

8x-40)/3=9x/5+30

x=50 master brush every day (8*50-40) 3=120 apprentice brush 90 per day set takes x days.

120+90*2）*x=36*50

x = 6 masters x people apprentices n people.

36*50/3=600=120x+90y

20=4x+3y y=(20-4x)/3

85x+65y=z=85x+65(20-4y)/3=（1300-5x）/3

x=2 y=4

4 questions can be found.

Solution: There is a 1 hour of work by x people.

Then there are (x+8) people working for 8 hours.

1.From the question, it can be seen that A does 1 25 every day, B does 1 20 every day, and A and B do 5 days 5x(1 25+1 20)=9 20

9 20 1 20 = 9 (days) Answer: B is doing it alone for five days.

2. Let each person's work rate be x, and the first batch of finishing personnel is y, then the total amount of work is 40x

40x=4xy+(y+2)8x

3. From the questions, it can be seen that the work efficiency of the first year of junior high school students is 2 15, and the work efficiency of the second year of junior high school students is 1 5

1-(1 15+1 5)] 1 5=11 3 1+11 3=14 3 (days) Answer: It takes 14 3 days in total.

The rest is pretty much the same, and you'll do it if you master the method.

It's so simple, I'm ashamed of you.

1 All (1) There are 31 people working in A and 20 people working in B, and 18 people are now transferred to support, so that the number of people working in A is twice as large as the number of people working in B, and how many people should be transferred to each of A and B.

If x people should be transferred to A, then 18-x people should be transferred to B.

31+x=2(20+18-x)

31+x=2(38-x)

31+x=76-2x

3x=45x=15

18-x=3

If 15 people should be transferred to A, 3 people should be transferred to B.

2) A tractor terried a piece of land, on the first day it stalked 1 4 of this land, on the second day it plowed the remaining 1 3 less 2 acres, on the third day it plowed the remaining 1 2 more than an acre, which is still 25 acres uncultivated, ask how many acres of this land are there?

This land has a total of x acres.

x-1/4x-(1/4x-2)-(1/4x+1)=253/4x-1/4x+2-1/4x-1=251/4x+1=25

1/4x=24

x=96 This piece of land has a total of 96 acres.

1.Set to X people in A. According to the conditions, the system of equations x+y=18, (31+x) (20+y)=2, and x=15, y=3 can be obtained

2.If there are x acres of land, then x 4 is plowed on the first day, (x 4)-2 is plowed on the second day, and (x 4)-1 is plowed on the third day, so (x 4)+(x 4)-2+(x 4)-1=x-25, and x=88 is obtained

1.Solution: It should take x hours to complete.

x(1 10+1 15)=1 (process omitted) x=6 A. It takes 6 hours to complete. 2.

Solution: Let all projects be x. The master can complete x 8 per day, and the apprentice can complete x 12 per day

Together, you can do 5x 24 per dayAfter four days, the total amount of work completed is 4*(5x 24)=5x 6The remaining engineering quantity is x-5x 6=x 6.

The number of days required for the apprentice to do it is = (x 6) (x12) = 2 days. Therefore, it is just done. 3.

Solution: Let A process x per hour, and B is x+2 then 4 (x+x+2)+6x=400 4x+4x+8+6x=400 14x=392 x=28 B: 28+2=30 Answer:

A 28, B 30