A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

45,000 fans x \( \frac{4}{5} \) = \( \frac{180000}{5} \) = 36,000 fans.

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

4\( \sqrt{32} \) - 3\( \sqrt{2} \)
4\( \sqrt{16 \times 2} \) - 3\( \sqrt{2} \)
4\( \sqrt{4^2 \times 2} \) - 3\( \sqrt{2} \)
(4)(4)\( \sqrt{2} \) - 3\( \sqrt{2} \)
16\( \sqrt{2} \) - 3\( \sqrt{2} \)

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

To multiply terms with radicals, multiply the coefficients and radicands separately:

8\( \sqrt{8} \) x 6\( \sqrt{3} \)
(8 x 6)\( \sqrt{8 \times 3} \)
48\( \sqrt{24} \)

Now we need to simplify the radical:

48\( \sqrt{24} \)
48\( \sqrt{6 \times 4} \)
48\( \sqrt{6 \times 2^2} \)
(48)(2)\( \sqrt{6} \)
96\( \sqrt{6} \)

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-8y^8}{9y^3} \)
\( \frac{-8}{9} \) y^{(8 - 3)}
-\(\frac{8}{9}\)y⁵

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 = \( \frac{300mi}{60mph} \)
5 hours