30 miles / 1 hour  *  5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec

Since $\displaystyle \dpi{100} \small \frac{1}{4}$ of the children are girls, this totals to $\displaystyle \dpi{100} \small 20 \times \frac{1}{4} = 5$ girls in the group.

$\displaystyle \dpi{100} \small 20-5=15$ boys.

Remember, when you multiply fractions, you can directly multiply their denominators and their numerators; therefore, you can begin this problem by making it into one large fraction:

$\displaystyle \frac{5}{7}*\frac{6}{4}*\frac{12}{2} = \frac{5*6*12}{7*4*2}$

Now, you could multiply all of this out and then divide. However, you can cancel things immediately. The $\displaystyle 4$ goes into the $\displaystyle 12$ and the $\displaystyle 2$ into the $\displaystyle 6$. Thus, you have:

$\displaystyle \frac{5*6*12}{7*4*2} = \frac{5*3*3}{7}=\frac{9*5}{7}=\frac{45}{7}$

First, begin by remembering that $\displaystyle 14$ is the same as $\displaystyle \frac{14}{1}$:

$\displaystyle \frac{15}{8}*\frac{12}{5}*\frac{1}{3}*\frac{14}{1}$

Next, recall that you multiply fractions by multiplying the numerators and denominators by each other. It is very simple. This would give you:

$\displaystyle \frac{15}{8}*\frac{12}{5}*\frac{1}{3}*\frac{14}{1}=\frac{15*12*1*14}{8*5*3}$

Now, you can cancel the $\displaystyle 15$ and the $\displaystyle 5*3$:

$\displaystyle \frac{15*12*1*14}{8*5*3} = \frac{12*14}{8}$

Next, you can reduce the $\displaystyle 8$ and the $\displaystyle 12$:

$\displaystyle \frac{3*14}{2}$

You can also reduce the resulting $\displaystyle 2$ and the $\displaystyle 14$:

$\displaystyle \frac{3*7}{1}=21$

1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

Finding the common denominator yields $\displaystyle \frac{24}{56}+\frac{35}{56}-\frac{28}{56}$. We can then evaluate leaving $\displaystyle \frac{31}{56}$.

$\displaystyle x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices $\displaystyle \tiny \tiny \frac{49}{109}$ and $\displaystyle \small \frac{30}{109}$ are out. Now, let's add the two fractions:

Begin by converting $\displaystyle \small 2 \frac{5}{6}$ to $\displaystyle \tiny \frac{17}{6}$.

Now find the common denominator of $\displaystyle \small \frac{4}{5}$ and $\displaystyle \tiny \frac{17}{6}$. The least common multiple of 5 and 6 is 30, so 30 is the common denominator. Now alter both fractions so that they use the common denominator:

$\displaystyle \tiny \small \frac{4}{5}= \frac{4*6}{5*6}=\frac{24}{30}$

 $\displaystyle \tiny \small \frac{17}{6}=\frac{17*5}{6*5}=\frac{85}{30}$

Now we can easily add the two fractions together:

$\displaystyle \small \frac{24}{30}+\frac{85}{30}=\frac{109}{30}$

The answer is $\displaystyle \small \frac{109}{30}$.