solving a real - world problem\nin a period of $2\\frac{1}{4}$ hours, $5\\frac{1}{2}$ gallons of water…

solving a real - world problem\nin a period of $2\\frac{1}{4}$ hours, $5\\frac{1}{2}$ gallons of water leaked from a water tank. how much water did the tank lose per hour?\nwhich division problem represents the problem?\n$\\frac{9}{4}\\div\\frac{11}{2}$\n$\\frac{4}{9}\\div\\frac{2}{11}$\n$\\frac{11}{2}\\div\\frac{9}{4}$\n$\\frac{11}{2}\\div\\frac{9}{4}$

solving a real - world problem\nin a period of $2\\frac{1}{4}$ hours, $5\\frac{1}{2}$ gallons of water leaked from a water tank. how much water did the tank lose per hour?\nwhich division problem represents the problem?\n$\\frac{9}{4}\\div\\frac{11}{2}$\n$\\frac{4}{9}\\div\\frac{2}{11}$\n$\\frac{11}{2}\\div\\frac{9}{4}$\n$\\frac{11}{2}\\div\\frac{9}{4}$

Answer

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert (2\frac{1}{4}) to an improper fraction. (2\frac{1}{4}=\frac{2\times4 + 1}{4}=\frac{9}{4}). Then, convert (5\frac{1}{2}) to an improper fraction. (5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}).

Step2: Determine the division operation

To find the amount of water lost per hour, we divide the total amount of water leaked ((\frac{11}{2}) gallons) by the total time ((\frac{9}{4}) hours). So the division problem is (\frac{11}{2}\div\frac{9}{4})? Wait, no, wait. Wait, actually, the time is (2\frac{1}{4}=\frac{9}{4}) hours, and the water leaked is (5\frac{1}{2}=\frac{11}{2}) gallons. To find per hour, we do total water divided by total time, so (\frac{11}{2}\div\frac{9}{4})? Wait, no, let's check the options. Wait, the options are:

  1. (\frac{9}{4}\div\frac{11}{2})
  2. (\frac{4}{9}\div\frac{2}{11})
  3. (\frac{11}{2}\div\frac{9}{4})
  4. (\frac{11}{2}\div\frac{9}{4}) (Wait, the fourth option is (-\frac{11}{2}\div\frac{9}{4}), but since we are dealing with positive quantities, we can ignore the negative. Wait, the problem is about how much water lost per hour, so it's total water (positive) divided by total time (positive). So total water is (5\frac{1}{2}=\frac{11}{2}), total time is (2\frac{1}{4}=\frac{9}{4}). So the division is (\frac{11}{2}\div\frac{9}{4}), which is the third option (the third option is (\frac{11}{2}\div\frac{9}{4}), and the fourth is with a negative sign, which doesn't make sense here). Wait, let's re-express:

Wait, the question is "Which division problem represents the problem?" So we need to find which division is total water divided by total time. Total water: (5\frac{1}{2}=\frac{11}{2}) gallons. Total time: (2\frac{1}{4}=\frac{9}{4}) hours. So per hour loss is (\frac{11}{2}) gallons (\div) (\frac{9}{4}) hours, which is (\frac{11}{2}\div\frac{9}{4}), which is the third option (the option labeled as (\frac{11}{2}\div\frac{9}{4})). Wait, looking at the options:

First option: (\frac{9}{4}\div\frac{11}{2}) (time divided by water, not correct)

Second option: (\frac{4}{9}\div\frac{2}{11}) (not related)

Third option: (\frac{11}{2}\div\frac{9}{4}) (water divided by time, correct)

Fourth option: (-\frac{11}{2}\div\frac{9}{4}) (negative, not correct as loss is positive)

So the correct division is (\frac{11}{2}\div\frac{9}{4}), which is the third option (the one with (\frac{11}{2}\div\frac{9}{4})).

Wait, let's confirm:

To find rate (gallons per hour), we use rate = amount / time.

Amount = (5\frac{1}{2}=\frac{11}{2}) gallons.

Time = (2\frac{1}{4}=\frac{9}{4}) hours.

So rate = (\frac{11}{2}\div\frac{9}{4}), which is the third option (the option with (\frac{11}{2}\div\frac{9}{4})).

Answer:

The correct option is the one with (\frac{11}{2}\div\frac{9}{4}) (assuming the third option is labeled as such, e.g., if the options are A, B, C, D, then if C is (\frac{11}{2}\div\frac{9}{4}), then the answer is C. (\frac{11}{2}\div\frac{9}{4}))