Convert the two liters of soda into ounces.

\(\displaystyle 2 * 33.814 = 67.628\)

Subtract the four eight-ounce glasses of soda that were poured.

\(\displaystyle 67.628 - (4*8)=35.628\)

Convert the remaining ounces back into liters.

\(\displaystyle 35.628 * \frac{1}{33.814} = 1.05\)

Alternatively, you could set it up as one equation and solve for \(\displaystyle x\), as shown below.

\(\displaystyle x = 2 - [(8\times 4)\times\tfrac{1}{33.814}]\)

\(\displaystyle x = 2 - 0.95\)

\(\displaystyle x=1.05\)

To replace hours with seconds, you must divide by 3600 (seconds in an hour), and to replace miles with feet you must multiply by 5280 (number of feet in a mile).

This problem relies on the formula \(\displaystyle \textup{distance = rate * time}\), or \(\displaystyle d = rt\).

Solving for \(\displaystyle t\) in the case of both Edward's original trip and the trip Edward will take this time will give us the time each trip would take. The difference between these times is the answer.

The distance Edward travels is \(\displaystyle 225\) miles. The rate at which he drives on the first trip is \(\displaystyle 60\) miles per hour. Remember that in writing out equations we can treat the word "per" as a division sign, so we express \(\displaystyle 60 \textup{ miles per hour}\) as \(\displaystyle \frac{60 \ miles}{1 \ hour}\). Solve for \(\displaystyle t\) with these numbers in \(\displaystyle d = rt\).

\(\displaystyle 225 \ miles = (\frac{60 \ miles}{1 \ hour}) * (t \ hours)\)

\(\displaystyle (225 \ miles) * (\frac{1 \ hour}{60 \ miles}) = (\frac{60 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{60 \ miles})\)

\(\displaystyle \frac{225}{60} \ hours = t \ hours\)

\(\displaystyle t = \frac{15}{4} \ hours = 3\tfrac{3}{4} \ hours\)

To convert the remainder fraction of an hour into minutes, multiply it by \(\displaystyle 60 \ minutes \ per \ hour\).

\(\displaystyle \frac{3}{4} \ hours * \frac{60 \ minutes}{1 \ hour} = \frac{180}{4} \ minutes = 45 \ minutes\)

So the total time for the original trip is \(\displaystyle 3\) hours and \(\displaystyle 45\) minutes.

Now use the same \(\displaystyle d = rt\) equation, but replace the \(\displaystyle 60\) miles per hour with \(\displaystyle 75\) miles per hour for the second trip.

\(\displaystyle 225 \ miles = (\frac{75 \ miles}{1 \ hour}) * (t \ hours)\)

\(\displaystyle (225 \ miles) * (\frac{1 \ hour}{75 \ miles}) = (\frac{75 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{75 \ miles})\)

\(\displaystyle \frac{225}{75} \ hours = t \ hours\)

\(\displaystyle t = 3 \ hours\)

We now know the trip at \(\displaystyle 75\) miles per hour would be \(\displaystyle 3\) hours long. Subtracting this from the length of the original \(\displaystyle 60\) miles per hour trip gives us the amount of time by which this trip would be shorter than the original.

\(\displaystyle (3 \ hours, 45 \ minutes) - (3 \ hours) = 45 \ minutes\)

To compare these three different measurements, we need to convert them so they have the same units. Let's convert all three values into meters per second.

Multiplying 70 km/h by 1000 m/km gives us 70,000 meters per hour, and dividing that value by 3600 (since there are 3600 seconds in an hour) gives us 19.4. So, Albert is traveling at 19.4 meters per second.

We convert Katrina's speed in a similar way, multiplying 1.9 km/minute by 1000 m/km and then dividing by 60 (since there are 60 seconds in a minute). These calculations give us 31.67 m/s.

Since both of these values are slower than Joseph's speed of 35 m/s, Joseph is traveling the fastest.

1 meter is equal to 100 centimeters, so 1 cubic meter is equal to \(\displaystyle 100^{3} = 1,000,000\) cubic centimeters.

1,000,000 cubic centimeters has mass:

\(\displaystyle 1,000,000 \textrm{\;cm}^{3} \cdot X \frac{\textrm{g}}{\textrm{cm}^{3}} = 1,000,000X \textrm{\; g}\)

1,000 grams are in a kilogram, so convert to kilograms by dividing this number by 1,000:

\(\displaystyle 1,000,000 X \div 1,000 = 1,000 X\)

Let  \(\displaystyle x\) be the number of map centimeters that represent \(\displaystyle N\) kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for \(\displaystyle x\)

\(\displaystyle \frac{x}{N} = \frac{3}{45}\)

\(\displaystyle \frac{x}{N} = \frac{1}{15}\)

\(\displaystyle \frac{x}{N} \cdot N = \frac{1}{15}\cdot N\)

\(\displaystyle x = \frac{N}{15}\)

Let  \(\displaystyle x\) be the number of map centimeters that represent \(\displaystyle N\) kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for \(\displaystyle x\)

\(\displaystyle \frac{x}{N} = \frac{3}{66}\)

\(\displaystyle \frac{x}{N} = \frac{1}{22}\)

\(\displaystyle \frac{x}{N} \cdot N = \frac{1}{22}\cdot N\)

\(\displaystyle x = \frac{N}{22}\)

Let  \(\displaystyle x\) be the number of actual kilometers represented by \(\displaystyle N\) map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{N} = \frac{66}{3}\)

\(\displaystyle \frac{x}{N} = 22\)

\(\displaystyle \frac{x}{N} \cdot N = 22 \cdot N\)

\(\displaystyle x = 22N\)

Let  \(\displaystyle x\) be the number of actual kilometers represented by \(\displaystyle N\) map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{N} = \frac{45}{3}\)

\(\displaystyle \frac{x}{N} = 15\)

\(\displaystyle \frac{x}{N} \cdot N = 15 \cdot N\)

\(\displaystyle x = 15N\)

15% is equal to \(\displaystyle \small \frac{15}{100}\), or 0.15. We can find the amount of the increase by multiplying the original cost by 0.15.

\(\displaystyle 240*0.15=36\)

The new amount is the sum of the original amount and the increase.

\(\displaystyle \small 240+36=276\)

This gives us the new cost for one week. The cost for the new month will be four times this amount.

\(\displaystyle \small 276*4=1104\)