The easiest way to solve this is with a rate formula: 1 / combined time = 1 / Bob's time + 1 / Ron's time.  We know the combined time and Bob's time, so we can solve for Ron's time:

1/2 = 1/3 + 1/Ron's time

1/Ron's time = 1/2 – 1/3 = 1/6

Ron's time = 6 hours 

Although it seems as though "Quantity B is greater" is the correct answer at first glance, a further analysis indicates that this answer is a trap. If $\displaystyle x$ and $\displaystyle y$ are negative numbers, such as $\displaystyle -2$ and $\displaystyle -3$, then $\displaystyle x$ would be the larger number. Similarly, $\displaystyle y$ is larger if both $\displaystyle x$ and $\displaystyle y$ are positive numbers. Thus, it cannot be determined which variable is larger simply based on the information given.

First count the total number of parts in the ratio.

$\displaystyle 6+3+5=14$

Then we can set up a proportion representing $\displaystyle \frac{number\ of\ pennies}{number\ of\ coins}$. 

As the initial ratio shows, there are 6 pennies for every 14 total coins. In the total set, we have X pennies and 42 total coins. Plugging these numbers into the proportion gives $\displaystyle \frac{6}{14}=\frac{x}{42}$.

Finally, we multiply both sides times 42 to isolate x.

$\displaystyle \frac{6}{14}*42=\frac{x}{42}*42$

$\displaystyle 18=x$

2 gallons of lemonade equals 8 quarts of lemonade. To make 3 quarts of lemonade, you need $\displaystyle \frac{3}{8}$ of the amount needed to make 2 gallons of lemonade, or 6 ounces of mix.

This problem states that there are $\displaystyle 40$ students in the class taking Calculus. Because the class has a total of $\displaystyle 50$ students, that means there are only $\displaystyle 10$ students in the class not taking Calculus. The problem also states that there are $\displaystyle 15$ students in the class taking Chinese. Because only $\displaystyle 10$ students in the class aren't taking Calculus, this means that there is a minimum of $\displaystyle 5$ students in the class that are taking both Calculus and Chinese.

For this problem, you must do conversions of from hours to seconds.  

Two hours is equal 120 minutes 

$\displaystyle (2*60=120)$.  

120 minutes is equal to 7200 second 

$\displaystyle (120*60=7200)$.

The train travels 8 feet per second so in 7200 seconds it travels 57600 feet 

$\displaystyle (7200*8=57600)$.

When selecting ratios for two variables (boys and girls) the two sides of the ratio must add up to be a factor of the total student count.  The factors of 28 include 14, 7, 4, and 2.  (1 + 1 = 2), (2 + 3 = 5), (3 + 4 = 7), and (1 + 3 = 4). 5 is the only nonfactor and cannot be the ratio of boys to girls, thus making 2 : 3 the correct answer.

Since 40 loaves of bread are sold daily, and the ratio of bread to cakes is 5:2, then $\displaystyle \dpi{100} (40\div 5)\cdot 2=16$ cakes are sold daily.

Using the ratio in the same way, we can find the additional amount of cakes sold:

 $\displaystyle \dpi{100} (12\div 5)\cdot 2=4.8\approx 5$ cakes with approximation.

Thus, the total amount of cakes sold on Tuesday is $\displaystyle 16+5=21$ cakes. 

One teaspoon of salt requires 2 teaspoons of baking powder, which requires 16 teaspoons of milk and 32 teaspoons of sugar. 32 teaspoons of sugar requires 96 teaspoons of flour, which equals two cups of flour.

First, you have to set up the given ratios, which is 3 cookies : 2 cupcakes and 5 cookies : 6 pastries. Then, you find a common multiple of cookies (i.e. 15) and convert the ratios to 15 cookies : 10 cupcakes and 15 cookies : 18 pastries. Since both ratios now have 15 cookies, you can infer that the ration of cupcakes to pastries is 10:18 or 5:9.