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Seven Answers to Math Workbooks
6. Let the speed of A be x cycles per minute and the speed of B be y cycles per minute to obtain the equation:

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.