Suppose the distance between AB and x.
x-(x/4)=x-72
x=288
A: The distance between A and B is 288 meters.
Each worker in a workshop can produce 12 bolts or 18 nuts, and each bolt should be equipped with two nuts. There are currently 28 workers. How to allocate the number of workers to make the daily output just match?
Solution:? Let x people be assigned to produce bolts, and then (28-x) people produce nuts.
Because each bolt has two nuts, there are twice as many bolts as nuts.
?
? 2× 12x= 18(28-x)
? Solve? x= 12？ Lock 28-x=28- 12= 16
That is, 12 people should be allocated to produce bolts and 16 people to produce nuts.
It is known that five A-type machines have 8 boxes full of products, and 47 B-type machines have 1 1 boxes full of products, leaving 1 box. Each type A machine produces 1 product more than the type B machine. How many products are there in each box?
Suppose there are x products in each box.
5 Type A machines: 8x+4
7 B model: 1 1x+ 1.
Because (8x+4)/5 = (11x+1)/7+1.
Institute: x= 12
Each box contains 12 products.
To process 200 parts, A will work alone for 5 hours, and then work with B for 4 hours to complete the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process per hour?
Solution: Let B process (x-2) every hour, then A processes X every hour.
According to the total amount of work such as work efficiency and time:
[(X-2)+X]*4+5X=200
[2X-2]*4+5X=200
8X-8+5X=200
13X=200+8
13X=208
X=208/ 13
X = 16...A.
16-2 = 14 () ...b
A: Then A handles 16 per hour, and B handles 14 per hour.
The total length of the bridge is 1000m, and a train passes through the bridge. It takes 1 minute for the train to cross the bridge completely from the beginning, and it takes 40 seconds for the whole train to cross the bridge completely. Find the speed and length of the train.
1 min =60 seconds
If the length of the train is x meters, according to the meaning of the question.
Train speed (1000+x)/60
Therefore [(1000+x)/60] * 40 =1000-2x.
The solution is x= 125.
( 1000+x)/60 =( 1000+ 125)/60 = 1 125/60 = 18.75
The train speed is18.75m per second and the length is125m.
As shown in the figure, in ABC, D is on AB, and δδCAD and δδCBE are equilateral triangles. Proof: (1)DE=AB, (2) ∠ EDB = 60?
2. As shown in the figure, in Δ δABC, AD bisects ∠BAC, DE||AC,EF⊥AD passes through BC and extends at F. Proof: ∠FAC=∠B?
?
3. As shown in the figure, in △ ABC, AD and AE are the bisectors of the height and angle of △ ABC respectively. If ∠B=30?
∠ c = 50, find: (1), find the degree of ∠DAE. (2) What is the relationship between ∠ DAE and ∠C-∠B? (No proof required)
4, the shape of the parts as shown in the figure, according to the provisions ∠A=90? ，∠ C=25？ ，∠B=25？ , check the measured ∠BDC= 150? , judge that the part is unqualified, and explain the reason of the unqualified part with the knowledge of triangle. ?
5. As shown in the figure, DF∨AC and ∠ C = ∠ D are known. Can you judge CE∨BD? Try to explain your reasons?