Question
This week, Sam will run 2 1/4 miles on Monday, 3 5/6 miles on Tuesday, and 4 miles on
Wednesday. Next week, Sam will run the same number of miles on Monday, Tuesday, and
Wednesday. What is the total number of miles Sam will run over these 6 days? Record your
answer as a mixed number
___
Wednesday. Next week, Sam will run the same number of miles on Monday, Tuesday, and
Wednesday. What is the total number of miles Sam will run over these 6 days? Record your
answer as a mixed number
___
Answers
GPT-4o mini
To find the total number of miles Sam will run over these 6 days, we first need to determine the total mileage for each week (Monday, Tuesday, and Wednesday) and then multiply that by 2, as he will run the same distance next week.
**Step 1: Convert the mixed numbers to improper fractions.**
1. For Monday:
\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]
2. For Tuesday:
\[
3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6}
\]
3. For Wednesday:
\[
4 = \frac{4}{1} = \frac{4 \times 6}{6} = \frac{24}{6}
\]
**Step 2: Find a common denominator and add the fractions.**
The least common multiple of 4 and 6 is 12. Now we convert each fraction to have a denominator of 12.
1. Monday's distance:
\[
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
\]
2. Tuesday's distance:
\[
\frac{23}{6} = \frac{23 \times 2}{6 \times 2} = \frac{46}{12}
\]
3. Wednesday's distance:
\[
\frac{24}{6} = \frac{24 \times 2}{6 \times 2} = \frac{48}{12}
\]
**Step 3: Add the distances together.**
Now, sum the distances:
\[
\frac{27}{12} + \frac{46}{12} + \frac{48}{12} = \frac{27 + 46 + 48}{12} = \frac{121}{12}
\]
**Step 4: Convert the total into a mixed number.**
Divide 121 by 12:
- \(121 \div 12 = 10\) with a remainder of \(1\).
Thus:
\[
\frac{121}{12} = 10 \frac{1}{12}
\]
**Step 5: Calculate the total for 2 weeks.**
Since Sam will run this total for 2 weeks:
\[
2 \times \frac{121}{12} = \frac{242}{12}
\]
Now simplify \(\frac{242}{12}\):
- \(242 \div 12 = 20\) with a remainder of \(2\).
Thus:
\[
\frac{242}{12} = 20 \frac{2}{12} = 20 \frac{1}{6}
\]
**Final Answer:**
The total number of miles Sam will run over the 6 days is:
\[
\boxed{20 \frac{1}{6}}
\]
**Step 1: Convert the mixed numbers to improper fractions.**
1. For Monday:
\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]
2. For Tuesday:
\[
3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6}
\]
3. For Wednesday:
\[
4 = \frac{4}{1} = \frac{4 \times 6}{6} = \frac{24}{6}
\]
**Step 2: Find a common denominator and add the fractions.**
The least common multiple of 4 and 6 is 12. Now we convert each fraction to have a denominator of 12.
1. Monday's distance:
\[
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
\]
2. Tuesday's distance:
\[
\frac{23}{6} = \frac{23 \times 2}{6 \times 2} = \frac{46}{12}
\]
3. Wednesday's distance:
\[
\frac{24}{6} = \frac{24 \times 2}{6 \times 2} = \frac{48}{12}
\]
**Step 3: Add the distances together.**
Now, sum the distances:
\[
\frac{27}{12} + \frac{46}{12} + \frac{48}{12} = \frac{27 + 46 + 48}{12} = \frac{121}{12}
\]
**Step 4: Convert the total into a mixed number.**
Divide 121 by 12:
- \(121 \div 12 = 10\) with a remainder of \(1\).
Thus:
\[
\frac{121}{12} = 10 \frac{1}{12}
\]
**Step 5: Calculate the total for 2 weeks.**
Since Sam will run this total for 2 weeks:
\[
2 \times \frac{121}{12} = \frac{242}{12}
\]
Now simplify \(\frac{242}{12}\):
- \(242 \div 12 = 20\) with a remainder of \(2\).
Thus:
\[
\frac{242}{12} = 20 \frac{2}{12} = 20 \frac{1}{6}
\]
**Final Answer:**
The total number of miles Sam will run over the 6 days is:
\[
\boxed{20 \frac{1}{6}}
\]