Solution: Assuming that the total amount of the project is 1, it takes X days for Party A to do it alone and Y days for Party B to do it alone.
As we all know, a project can be completed by Party A alone for 63 days and then by Party B alone for 28 days, so
63/x + 28/y = 1
If both parties cooperate, it will take 48 days to complete, so
48/x + 48/y = 1
x = 84，y = 1 12
B Need (1-42/84)/(112) = 56.
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2. Eight identical rectangles make a big rectangle with an area of 750 square centimeters. What is the circumference of this big rectangle? (Answer: 1 15)
Solution:
Suppose that the length of each small rectangle is x and the width is y,
Then there are four cases of perimeter.
4x+8y，8x+4y，2x+ 16y， 16x+2y
It is known that only the area, no aspect ratio, must have four cases of perimeter.
How can there be an answer and only one result?
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3. Six digits, divisible by 9 and 1 1. Remove the first two digits and the last two digits of this six-digit number, and the middle four digits are 1997. So what is this six-digit number? (answer: 2 19978)
Solution:
Suppose the 100 thousand digits are x
This number = x *100000+19970+y.
= x( 10 10 * 99+ 10)+(20 1 * 99+7 1)+y
=( 10 10x+20 1)* 99+ 10x+7 1+y
Is a multiple of 1 1*9 = 99.
So 10x+7 1+y is a multiple of 99.
10 max 90, y max 9, plus 7 1 or multiples of 99.
So 10x+7 1+y = 99.
10x + y = 28
x= 1，y = 18 & gt； 9 untenable
X=2, y=8 holds.
x=3， 10x = 30 & gt； 28 does not hold water
So x = 2 and y = 8.
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4. If the first, second and third teams cooperate, it will take 12 days to complete a project; If the first, third and fifth teams of Qi Xin work together, it will take 7 days to complete; If the second, fourth and fifth teams work together, it will take 8 days to complete; If the first, third and fourth teams work together, it will take 42 days to complete. So how many days will it take for these five teams to work together to complete this project? (Answer: 6)
Solution:
Assuming that it takes abcde days for the 12345 team to complete independently, then it is known by the
1/a+ 1/b+ 1/c = 1/ 12-( 1)
1/a+ 1/c+ 1/e = 1/7-(2)
1/b+ 1/d+ 1/e = 1/8-(3)
1/a+ 1/c+ 1/d = 1/42-(4)
From (1)(2)(4)
1/a+ 1/c = 1/ 12- 1/b = 1/7- 1/e = 1/42- 1/d = t
112+1/7+1/42 is obtained by subtracting both sides of (3).
1/ 12- 1/b+ 1/7- 1/e+ 1/42- 1/d
= 1/ 12 + 1/7 + 1/42 - 1/8
3t = 1/ 12+ 1/42+ 1/56 = 1/8
t = 1/24
So1/a+1/b+1/c+1/d =1/e.
= 1/a+ 1/c+ 1/8 = 1/24+ 1/8 = 4/24 = 1/6
So it takes six days.
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5. The pool can be filled with water from two water pipes A and B. It takes 12 hours to fill single pipe A and 24 hours to fill single pipe B. Now, it is required to fill the pool with 10 hours, and the less time it takes for two pipes A and B to be put together, the better. So how many hours does it take for two pipes A and B to be put together at least? (Answer: 4)
Solution:
A is released per hour112, and b is released per hour 1/24, indicating that A is released quickly, and A in a single release is needed for a short release time. Assume that X hours are released together, and A is released for (10-x) hours, which is equivalent to 10 hour.
10/ 12 + x/24 = 1
x = 4