Since $\displaystyle DE = \frac{1}{2} (CD)$, $\displaystyle CD = 2 (DE)$

Since $\displaystyle CD = BC + 6$, $\displaystyle BC = CD - 6 = 2 \cdot DE - 6$, and, subsequently, $\displaystyle AB = 2 (DE) - 6$

$\displaystyle AE = AB + BC + CD + DE$

$\displaystyle = [2 \left (DE \right ) -6 ]+ [2 \left (DE \right ) -6 ] + 2 \left (DE \right ) + DE$

$\displaystyle = 2 \left (DE \right )+ 2 \left (DE \right ) + 2 \left (DE \right ) + 1\left ( DE \right ) -6 -6$

$\displaystyle = 7 \left (DE \right ) - 12$

To find the height of each box set the 3 boxes equal to the height of Big Bob. So, let $\displaystyle x$ be the height of each box. Then,

$\displaystyle 3x=8\ feet$ or $\displaystyle x=\frac{8\text{ feet}}{3}= 2.66\text{ feet}$

Therefore to find the maximum number of boxes that fit under the ceiling, we divide the ceiling height by the height of each box. So,

$\displaystyle \frac{55'}{2.66'} = 20.68$ or 20 whole boxes would fit under the ceiling.

$\displaystyle Original\ area=l\cdot w$

$\displaystyle New\ area=1.2l\cdot 1.2w$

$\displaystyle New\ area=1.44\cdot l\cdot w$

$\displaystyle 1.44-1=0.44$

$\displaystyle .44\cdot *100=44\%$

Area of Bedroom A is equal to area of Bedroom B, therefore:

$\displaystyle 6'*8'$$\displaystyle =10'*l$

$\displaystyle l=\frac{6'*8'}{10'}$

$\displaystyle l$$\displaystyle =4.8'$

One mile is equal to 5,280 feet, and one hour is equal to 3,600 seconds, The speed can be converted as follows:

$\displaystyle \frac{200 \textrm{ ft}}{1\textrm{ sec}} = \frac{200 \textrm{ ft } \times 3,600 \textrm{ sec / hr} }{1\textrm{ sec} \times 5,280 \textrm{ ft / mi } }$

$\displaystyle = 136 \frac{4}{11} \textrm{ mi / hr}$

or, rounded, 136 miles per hour.

1,000 nautical miles are equal to $\displaystyle 1,852 \times 1,000 = 1,852,000$ meters, or 

1 statute mile is equal to 1.609 kilometers, or 1,609 meters; divide 1,852,000 meters by 1,609 meters per statute miles to get

$\displaystyle 1,852,000 \div 1,609 \approx 1,151$ statute miles, the equivalent of 1,000 nautical miles.

1.609 kilometers, or 1,609 meters, are equal to a mile. One furlong, or one eighth of a mile, is equal to one eighth of 1,609 meters, or

$\displaystyle 1,609 \cdot \frac{ 1}{8} = 1,609 \cdot 0.125 = 201.125 \approx 201.1$ meters.

The first step is to convert the distance into feet:

 $\displaystyle 110\ yds * \frac{3\ ft}{1\ yd} = 330\ ft.$

Then, divide the distance by the baseball's rate of travel:

$\displaystyle \frac{330 ft}{75\ ft/sec} = 4.4\ sec.$

The formula to find the average speed is $\displaystyle avg.\ speed = \frac{total\ distance}{total\ time}$.

Since the question deals with miles per hour, the time must be converted to hours from minutes:

$\displaystyle \frac{75\ min}{60\ min}= 1.25\ hours$

Plugging the numbers into the equation gives $\displaystyle \frac{50\ miles}{1.25\ hours}= 40\ mph$.

One mile is equal to 5,280 feet, and one hour is equal to 3,600 seconds, The speed can be converted as follows:

$\displaystyle \frac{100 \textrm{ mi}}{1\textrm{ hr}} = \frac{100 \textrm{ mi } \times 5,280 \textrm{ ft / mi } }{1\textrm{ hr} \times 3,600 \textrm{ sec / hr}}$

$\displaystyle = 146 \frac{2}{3} \textrm{ ft / sec }$

 or, rounded, 147 feet per second.