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Mathematical problems (work efficiency) To make a batch of parts, the efficiency ratio of Party A and Party B is 3:4, and it takes 16 days for Party A to complete this batch of parts alone, so how many days does it take for two people to cooperate? The hound found a rabbit running in front of it 10 meters away, and immediately caught up with it. The hound had a big step. It ran 5 steps, and the rabbit had to run 9 steps, but the rabbit was fast. When the hound ran 2 steps, the rabbit could run 3 steps. How many meters could the hound catch up with the rabbit?
To make a batch of parts, the efficiency ratio of Party A and Party B is 3:4. It takes 16 days for Party A to complete this batch of parts alone, so how many days does it take for two people to cooperate? Efficiency of Party A: 1 / 16, each: (1 / 16) / 3 = 1 / 48, efficiency of Party B: (1 / 48) X4 = 1 / 12, cooperation of two people: 1 / (1 / 12 + 1 / 16) = 48 / 7 (days)
The efficiency of a is 1 / 16, the efficiency of B is (1 / 16) / 3 * 4 = 1 / 12
Days of cooperation between Party A and Party B
1/(1/12+1/16)=48/7
1 / 16 a day
The efficiency ratio is 3:4
So 1 / 16: B = 3:4
B = 1 / 12
Therefore, the cooperation between Party A and Party B takes 1 / (1 / 12 + 1 / 16) = 48 / 7 days, about 7 days
Is there a leak in your supplementary data?
16*3=48 …… General task
48 / (3 + 4) = 48 / 7 = 6 and 6 / 7 days How many days does it take for two people to work together
(1) The efficiency of a is
1/16
The efficiency of B is
（1/16）/3*4=1/12
Efficiency and efficiency
1/12+1/16=7／48
Days of cooperation
1 / (7 / 48) = 48 / 7 days
(2) 15 meters
The efficiency of a is
1 divided by 16 = 1 / 16
The efficiency of B is
（1/16）/3*4=1/12
Efficiency and efficiency
1/12+1/16=7／48
Days of cooperation
1 / (7 / 48) = 48 / 7 days
To solve the equations: 3x − 2Y = 8y + 4x = 7
If equation (2) is y = 7-4x, substituting the first equation (1) is 3x-2 (7-4x) = 8, the solution is x = 2, substituting x = 2 into y = 7-4x is y = - 1, then the solution of the system is x = 2Y = - 1
Work efficiency formula (percentage)
Lao Li used to make 800 parts in 5 hours, but now 900 parts in 4.5 hours. How many percentage points does his work efficiency increase?
“jerryzhang9”：
Original (800 pieces / hour) = 160 pieces
Now (900 pieces / 4.5) = 200 pieces / hour
The work efficiency is increased by (200-160) △ 160 = 40 △ 160 = 0.25 = 25%
Good luck and goodbye
Solutions of 4x + y = 6 and 3x + 2Y = 7
X-Y = - 1 is obtained from ① - ②
That is, x = Y-1
Substituting 4x + y = 6 leads to
4(y-1)+y=6
5y=10
Y=2
Then x = Y-1 = 1
The solution is as follows
X=1
Y=2
x=1，y=2
X=1 Y=2
4x+y=6…… (1)
3x+2y=7…… II.
① * 2 - 2 gives 5x = 5 = > x = 1
Substituting into 1, we get 4 + y = 6 = > y = 2
Party A and Party B make the same parts. Each of them can make one part every three minutes. Party A takes two minutes to make two parts, and Party B takes one minute to make three parts. Now they have to complete the task of making 202 parts together. How many minutes does it take at least?
If you want to use the least time, you should let two people cooperate to make: 2 × 3 + 2 = 8 minutes, that is, the efficiency of a is 28, 3 × 3 + 1 = 10 minutes, that is, the efficiency of B is 310; two people cooperate, the efficiency is 28 + 310 = 1120, that is, two people can make 11 parts in 20 minutes Four, that is, two people and two people can do 18 at the same time, 11 × 18 = 198 in 20 minutes, there are four left, four left, one person and two, it takes 2 × 3 = 6 minutes to complete, a total of 20 × 18 + 6 = 366 (minutes). A: at least 366 minutes
3x + y = 10,4x-2y = 7 Solution
6X+2Y=20
4X-2Y=7
10X=27
X=2.7
solution
3X+Y=10 ①
4X-2Y=7 ②
① * 2 + 2 is 10x = 27, x = 2.7
Y=10-3X=10-8.1=1.9
For a job, it takes 20 hours for Party A to work alone, 4 hours for Party B to work alone, and 2 hours for Party C to work alone. If Party A and Party B work together for 10 hours first, how many hours will it take for Party C to work alone again?
I have a similar answer
It takes 20 hours for Party A to work alone, 4 hours more for Party B than for Party A, and 2 hours more for Party C than for Party A. if Party A and Party B work together for 10 hours, how many hours can Party C work alone?
It takes 24 hours for B to work alone and 12 hours for C to work alone
That is: A does 1 / 20 of the work per hour, B does 1 / 24 of the work per hour, C does 1 / 12 of the work per hour
Now set and work alone in X hours
A completed 1 / 20 × 10 = 1 / 2
B completed 1 / 24 × 10 = 5 / 12
C completed 1 / 12 × X
The whole work has been completed
Equation 1 / 2 + 5 / 12 + 1 / 12 x = 1
The solution of the equation is x = 1
So C worked alone for an hour
How to solve the 2 / 3x + 8 = 5 / 4x equation?
2/3x+8=5/4x
8x+96=15x
7x=96
x=96/7
5/4x-2/3x=8
15/12x-8/12x=8
7/12x=8
x=(12*8)/7
The entire equation is multiplied by 12x to eliminate the denominator
We get 8 + 96x = 15
96x=7
x=7/96
2/3x+8=5/4x
2/3x-5/4x=-8
8/12x-15/12x=-8
-7/12x=-8
x=(12*8)/7
x=96/7
2/3x+8=5/4x
8x+96=15x
7x=96
x=96/7
The work efficiency of the equation of one variable and one degree!
For a project, it takes 10 days, 12 days and 20 days for Party A, Party B and Party C to do it alone. Now party a sits alone for two days, Party B does it alone for several days, and Party A, Party B and Party C cooperate for another two days to finish all the work. How many days has Party B done
Set the power of a, B and C to one tenth, one twelfth and one twentieth
Then:
Set up: B do X days alone
4*1/10+2*1/20+(2+x)*1/12=1
X=4
So Party B did it for six days
B does it for six days, B does it for two days, a total of eight days, right
B does it for six days, B does it for two days, a total of eight days, right
Decompose the following formulas into factors: - 27x ^ 4 + 18x ^ 3-3x ^ 2 x ^ 4-1
-27x^4+18x^3-3x^2
=-3x^2(9x^2-6x+1)
=-3x^2(3x-1)^2
x^4-1
=(x^2+1)(x^2-1)
=(x^2+1)(x+1)(x-1)
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