Question
On average, Robert drinks start fraction, 5, divided by, 9, end fraction
9
5
of a 6-ounce glass of water in start fraction, 1, divided by, 15, end fraction
15
1
of an hour. How many glasses of water does he drink in one hour?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as whole numbers, fractions, or mixed numbers.
To enter a mixed number, press the “+” key or click the “Mixed Number” button.
0
0
glasses
hours
1
Enter your final answer as a whole number, fraction, or mixed number in simplest form.
9
5
of a 6-ounce glass of water in start fraction, 1, divided by, 15, end fraction
15
1
of an hour. How many glasses of water does he drink in one hour?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as whole numbers, fractions, or mixed numbers.
To enter a mixed number, press the “+” key or click the “Mixed Number” button.
0
0
glasses
hours
1
Enter your final answer as a whole number, fraction, or mixed number in simplest form.
Answers
GPT-4o mini
To find out how many glasses of water Robert drinks in one hour, we need to analyze the problem step by step.
1. **Understanding the Rates:**
- Robert drinks \(\frac{5}{9}\) of a 6-ounce glass of water in \(\frac{1}{15}\) of an hour.
2. **Calculate the amount of water he drinks in one hour:**
- To find out how many \(\frac{1}{15}\) hour segments fit into one hour, we calculate:
\[
1 \text{ hour} \div \frac{1}{15} \text{ hour} = 1 \times \frac{15}{1} = 15 \text{ segments}
\]
- This means that in one hour, he will go through 15 segments of \(\frac{1}{15}\) hours.
3. **Calculate glasses consumed in one hour:**
- Since he drinks \(\frac{5}{9}\) of a glass in each \(\frac{1}{15}\) hour segment, we need to multiply the amount he drinks in one segment by the number of segments in an hour:
\[
15 \text{ segments} \times \frac{5}{9} \text{ glasses/segment} = \frac{15 \times 5}{9} = \frac{75}{9}
\]
4. **Simplifying \(\frac{75}{9}\):**
- To simplify \(\frac{75}{9}\):
\[
\frac{75 \div 3}{9 \div 3} = \frac{25}{3}
\]
5. **Convert \(\frac{25}{3}\) into a mixed number:**
- \(\frac{25}{3} = 8\) R \(1\), so as a mixed number, it is \(8 \frac{1}{3}\).
Thus, Robert drinks \(8 \frac{1}{3}\) glasses of water in one hour.
**Final Answer:**
\(8 \frac{1}{3}\) glasses of water.
1. **Understanding the Rates:**
- Robert drinks \(\frac{5}{9}\) of a 6-ounce glass of water in \(\frac{1}{15}\) of an hour.
2. **Calculate the amount of water he drinks in one hour:**
- To find out how many \(\frac{1}{15}\) hour segments fit into one hour, we calculate:
\[
1 \text{ hour} \div \frac{1}{15} \text{ hour} = 1 \times \frac{15}{1} = 15 \text{ segments}
\]
- This means that in one hour, he will go through 15 segments of \(\frac{1}{15}\) hours.
3. **Calculate glasses consumed in one hour:**
- Since he drinks \(\frac{5}{9}\) of a glass in each \(\frac{1}{15}\) hour segment, we need to multiply the amount he drinks in one segment by the number of segments in an hour:
\[
15 \text{ segments} \times \frac{5}{9} \text{ glasses/segment} = \frac{15 \times 5}{9} = \frac{75}{9}
\]
4. **Simplifying \(\frac{75}{9}\):**
- To simplify \(\frac{75}{9}\):
\[
\frac{75 \div 3}{9 \div 3} = \frac{25}{3}
\]
5. **Convert \(\frac{25}{3}\) into a mixed number:**
- \(\frac{25}{3} = 8\) R \(1\), so as a mixed number, it is \(8 \frac{1}{3}\).
Thus, Robert drinks \(8 \frac{1}{3}\) glasses of water in one hour.
**Final Answer:**
\(8 \frac{1}{3}\) glasses of water.