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 = \( \frac{100mi}{50mph} \)
2 hours

If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{4} \) = 8\(\frac{3}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 19 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 19 x 2 = 38 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{38} \) = 12\(\frac{17}{19}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 9 + 13 = 22 cooks.

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

5\( \sqrt{2} \) x 8\( \sqrt{8} \)
(5 x 8)\( \sqrt{2 \times 8} \)
40\( \sqrt{16} \)

Now we need to simplify the radical:

40\( \sqrt{16} \)
40\( \sqrt{4^2} \)
(40)(4)
160

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

9\( \sqrt{175} \) + 4\( \sqrt{7} \)
9\( \sqrt{25 \times 7} \) + 4\( \sqrt{7} \)
9\( \sqrt{5^2 \times 7} \) + 4\( \sqrt{7} \)
(9)(5)\( \sqrt{7} \) + 4\( \sqrt{7} \)
45\( \sqrt{7} \) + 4\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

The amount of flour you need is (3 - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{24}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups