To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{68} \) = \( \frac{\frac{16}{4}}{\frac{68}{4}} \) = \( \frac{4}{17} \)

By buying two shirts, Roger will save $47 x \( \frac{25}{100} \) = \( \frac{$47 x 25}{100} \) = \( \frac{$1175}{100} \) = $11.75 on the second shirt.

To simplify a radical, factor out the perfect squares:

\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)

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 6 meters so the equation becomes: 2w + 2h = 6.

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

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

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