Mba-day5 Mathematics - application problems - engineering problems

1. Basic knowledge points

1.1 workload s, The work efficiency v, working hours t The relationship among the three

• workload = The work efficiency * working hours namely s = vt
• working hours = workload / The work efficiency namely t = s/v
• The work efficiency = workload / Time , namely v = s/t
  Important note ： Time t A certain , Efficiency is directly proportional to the total

1.2 Important conclusions

If Party A completes it alone, it needs m God , Party B needs to complete it alone n God , be

• 1. The efficiency of a is 1/m, The efficiency of B is 1/n
• 2. The efficiency of cooperation between Party A and Party B is : 1/m + 1/n ( Efficiency can be added or subtracted )
• 3. The time required for the completion of the cooperation between Party A and Party B is 1 /（1/m + 1/n）= mn / (m+n)

1.3 Train of thought

Encountered engineering quantity problems , Generally, the whole engineering quantity is ( Water discharge capacity ) See the unit 1, Then solve the problem proportionally according to the problem stem conditions .
It is usually assumed that the total amount （ The amount of work 、 Water discharge capacity ）= 1 Analyze
-【 Important formula 】 Total efficiency = Each efficiency algebra and

• The work efficiency = workload / working hours
• Total amount = Partial quantity / Its corresponding proportion

2. Example

• Example 1： Build a highway , Team a's separate construction requires 40 Days to complete , Team B needs to work alone 24 Days to complete , Now both teams are from 2 End start , The result is at the midpoint of the distance 7.5 km Meeting and completion , Then the length of this highway is （）km

 Explain ： Set the length of this highway  s km
 Construction by team a alone requires 40 Days to complete , The efficiency of team a is  s / 40
 Construction by team B alone requires 24 Days to complete , The efficiency of team B is  s / 24
 From now on, the two teams start from 2 End start , The result is at the midpoint of the distance 7.5 km Meeting and completion 
1.  From the efficiency, we know that team B is the most efficient 
2.  A and B are at the midpoint of the distance 7.5 km Meeting and completion , It means that this period of time is the same 
3.  The construction length of Party A is  s/2 - 7.5 km,  The construction length of team B is  s/2 + 7.5 km

 Therefore, the following relationship is obtained ： Time  =  workload  /  efficiency 
(s/2 - 7.5) / (s / 40) = （s/2 + 7.5）/ (s / 24)
(s/2 - 7.5) * (s / 24) = (s / 40) * （s/2 + 7.5）
(s/2 - 7.5) * (1/24) = (1 / 40) *（s/2 + 7.5）
(1/24) /  (1 / 40) = （s/2 + 7.5）/ (s/2 - 7.5)
5/3 = （s/2 + 7.5）/ (s/2 - 7.5)
s = 60 km

• Example 2： A project is jointly undertaken by Party A and Party B 30 Days can be done , Team a does it alone 24 Days later , Team B joins , The two teams work together 10 Days later , Team a transferred , Team B continued to do 17 Finish... In days . If the project is done by team a alone , You need to () God

 Explain ：
 According to the workload = working hours * The work efficiency 
 Let the working efficiency of Party A be x,  B. the working efficiency is y, The following relationships can be obtained quickly 
30x + 30y =  workload 
34x + 27y =  workload 
y = 4/3 x

 Bring the above proportion into ： nail 30 +  B 30 =  Quantities completed 
30x + 30 * 4/3 x =  workload 
70x =  workload 
70 =  workload /x =  working hours 

• Example 3： A unit carries out office decoration , If Party A and Party B cooperate , Need to be 10 Zhou finished . The man hour fee is 100 ten thousand , Company a first does 6 Company B will continue to do it in a week 18 Zhou finished , The man hour fee is 96 ten thousand , Ask company a for the weekly man hour cost （）

 Explain , Weekly man hour cost of company A x, Company B's weekly man hour expenses y
 If Party A and Party B cooperate , Need to be 10 Zhou finished . The man hour fee is 100 ten thousand , have to  10x+10y = 100
 Company a will do it first 6 Company B will continue to do it in a week 18 Zhou finished , The man hour fee is 96 ten thousand , have to 6x+18y=96
10x+10y = 100
6x+18y=96
 The most simplified is 
x+y =10
x+3y=16
 have to y =3, x =7, That is, the weekly man hour cost of company A  7 ten thousand