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

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 8 people needing transportation leaving 8 - 6 = 2 who will have to find other transportation.

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

\( \frac{1}{7} \) x \( \frac{2}{9} \) = \( \frac{1 x 2}{7 x 9} \) = \( \frac{2}{63} \) = \(\frac{2}{63}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 2}{6 x 2} \) - \( \frac{5 x 1}{12 x 1} \)

\( \frac{10}{12} \) - \( \frac{5}{12} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{10 - 5}{12} \) = \( \frac{5}{12} \) = \(\frac{5}{12}\)

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 = \( \frac{75mi}{15mph} \)
5 hours