The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 60 have in common.

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 11 people needing transportation leaving 11 - 6 = 5 who will have to find other transportation.

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 = \( \frac{400mi}{50mph} \)
8 hours

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{9 x 5}{3 x 5} \) + \( \frac{6 x 3}{5 x 3} \)

\( \frac{45}{15} \) + \( \frac{18}{15} \)

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

\( \frac{45 + 18}{15} \) = \( \frac{63}{15} \) = 4\(\frac{1}{5}\)

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.