The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.

The factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 the greatest factor 60 and 40 have in common.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 27 large cakes are needed for the party so \( \frac{27}{12} \) = 2\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 14 x 3 = 42 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{42} \) = 11\(\frac{3}{7}\) 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 3 + 12 = 15 cooks.

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

5\( \sqrt{5} \) x 7\( \sqrt{5} \)
(5 x 7)\( \sqrt{5 \times 5} \)
35\( \sqrt{25} \)

Now we need to simplify the radical:

35\( \sqrt{25} \)
35\( \sqrt{5^2} \)
(35)(5)
175

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