The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 24 meters so the equation becomes: 2w + 2h = 24.

Putting these two equations together and solving for width (w):

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{11 + 9 + 13 + 7}{4} \) = \( \frac{40}{4} \) = 10

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{8} \) ÷ \( \frac{4}{7} \) = \( \frac{1}{8} \) x \( \frac{7}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{8} \) x \( \frac{7}{4} \) = \( \frac{1 x 7}{8 x 4} \) = \( \frac{7}{32} \) = \(\frac{7}{32}\)

If 83% of the town's 37,000 voters cast ballots the number of votes cast is:

(\( \frac{83}{100} \)) x 37,000 = \( \frac{3,071,000}{100} \) = 30,710

The mayor got 78% of the votes cast which is:

(\( \frac{78}{100} \)) x 30,710 = \( \frac{2,395,380}{100} \) = 23,954 votes.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{140mi}{35mph} \)
4 hours