1/(x+y)=2
1/(x-y)=6
Simplify:
x+y= 1/2
x-y= 1/6
The solution is x= 1/3 and y= 1/6, so A runs 1/3 laps per minute and B runs 1/6 laps per minute.
7. Suppose that X block in part A and Y block in part B are needed to obtain the equation:
2x+y= 15①
x+2y= 18②
Two formulas have been added:
3x+3y=33
x+y= 1 1③
Use ①-③ to get x = 4；;
Y=7 with ②-③.
Therefore, four A-sections and seven B-sections are needed.
8. Set 1 vat to hold X bottles of wine.
1 The keg can hold wine.
5x+y=3
x+5y=2
X= 13/24，y=7/24。
1 vats can hold wine 13/24,
1 The keg can hold wine 7/24.
9.0. 1x+0.5y+ 1z=7
x+y+z= 15
0≤x≤ 10 0≤y≤ 10 0≤z≤ 10
The solution is 0.9x+0.5y=8, and x, y, z, y and z are all integers.
So x=5 or 10.
Obviously, when x= 10, y=-2 does not meet the requirements.
When x=5, y=7 and z=3.
So, take 5 pieces, 7 pieces and 3 pieces respectively.