To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{6 x 4}{2 x 4} \) + \( \frac{7 x 1}{8 x 1} \)

\( \frac{24}{8} \) + \( \frac{7}{8} \)

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

\( \frac{24 + 7}{8} \) = \( \frac{31}{8} \) = 3\(\frac{7}{8}\)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (4 + 5) ÷ 5 x 5 - 2²
P: 4 + (9) ÷ 5 x 5 - 2²
E: 4 + 9 ÷ 5 x 5 - 4
MD: 4 + \( \frac{9}{5} \) x 5 - 4
MD: 4 + \( \frac{45}{5} \) - 4
AS: \( \frac{20}{5} \) + \( \frac{45}{5} \) - 4
AS: \( \frac{65}{5} \) - 4
AS: \( \frac{65 - 20}{5} \)
\( \frac{45}{5} \)
9

To subtract these radicals together their radicands must be the same:

6\( \sqrt{63} \) - 9\( \sqrt{7} \)
6\( \sqrt{9 \times 7} \) - 9\( \sqrt{7} \)
6\( \sqrt{3^2 \times 7} \) - 9\( \sqrt{7} \)
(6)(3)\( \sqrt{7} \) - 9\( \sqrt{7} \)
18\( \sqrt{7} \) - 9\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 8h \)
480 miles

The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 20 are [1, 2, 4, 5, 10, 20]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 20 have in common.