The relationship between several quantities in an engineering problem

Productivity Working hours Total work, total work hours working hours, total work efficiency, total work efficiency working hours.

Example 1For a project, it takes 12 days for teams A and B to cooperate, 15 days for teams B and C to cooperate, and 20 days for teams A and C to complete.

Analysis: If this project is 1 unit, then the ergonomics of A, B and C cooperation, and the ergonomics of A, C and C cooperation, so the ergonomics of A, B, and C teams cooperate twice, so the ergonomics of A, B, and C teams cooperate is twice as muchHence the time for the three teams to work together to complete the project.

Answer: It takes 10 (days) for teams A, B and C to cooperate.

Example 2A project takes 12 days to complete alone, and it takes 9 days for B to complete it alone If A does it for a few days and then B does it, and it takes 10 days to complete, ask A how many days has he done?

Analysis: When solving engineering problems, in addition to solving them with general arithmetic methods, you can also find the equiquantity relationship and solve the equation according to the conditions of the problem.

Solution (1): Let A do x days, then B does (10 x) days, A completes the workload, and B completes (10 x).

Therefore +(10 x) = 1 multiply 36 on both sides, simplifying, and getting: 3x 40 4x 36, x 4

A: A did it for 4 days.

Solution (2): By working with two people, it is necessary to: 1 (+=(day), because 5

In this way, it is not enough for each person to do 5 days, B must do more with high efficiency, and if B does 6 days, then A does 4 days.

So 6 + 4 = 1 meets the requirements. So A did it for 6 days.

A: A did it for 6 days.

Example 3A can do a job for 6 hours and B for 12 hours A can do it for 8 hours and B for 6 hours If A does it for 3 hours and B does it again, how many hours will it take to complete?

Analysis: Let a piece of work be completed in units "1" A does 6 hours and B does 12 hours to complete or A does 8 hours first and B does 6 hours again, and the relationship between them is shown in the diagram as follows

It is not difficult to see from the figure that A's 2-hour workload, B's 6-hour workload, A's 1-hour workload, B's 3-hour workload, can be solved by substitution method.

Solution: If B does it alone, it will take a total of 6 3 12 30 (hours).

If it is done by A alone: 8 6 3 10 (hours).

A does it for 3 hours, and then B needs to do it: (10 3) 3 21 (hours).

A: It will take 21 hours for B to complete.

Total amount of work worked hours = work efficiency.

Work efficiency * working hours = total amount of work.

Total amount of work (ergonomic sum) = joint time.

Ergonomics and * joint time = workload.

Work efficiency * working hours = total amount of work.

Total amount of work, work efficiency, working hours.

Total amount of work worked hours = work efficiency.

How many days ( ) did Team C participate in the construction of Project A

Select A6

Let the work efficiency of A be a, the work efficiency of B be b, and the specified time is x hours, then there is x(a+b)=1

9x[(1+20%)a+b]/10=1

x+ solution to the system of equations.

a=1/36

b=1/45

x=20 stipulates that the time is 20 hours.

The time it takes for A and B to meet is 1 (1 10+1 15)=6 (Hour God Remodeling).

Therefore, the distance between the eastern and western cities is 12 [(1 10-1 15) 6]=60 (km).

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It will take another 1 day to complete.

Assume the total amount of work w

A completes x every day, side B is also x, and C is not 4 3x

then there is w (2x+4 3x)=15

w/x=50 w=50x

And then again. 2x+2x+2*(4/3x)+20x+20x=140/3xw=50x)-140/3x=10/3x

A, B and C work together for a day with exactly less than 10 3x, so it still needs a day to complete.