Ortiz Wyatt
07/18/2023 · Junior High School
4) An owl travals \( 8_{3}^{1} \) milas in \( { }_{4}^{3} \) hour and a scagull travals \( 12{ }_{2}^{1} \) miles in \( { }_{3}^{2} \) hour 4) Complete each statement. 4) It takes the seagull ? time to travel a ? distance.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the problem, we first need to convert the given distances and times from their respective bases to base 10 (decimal).
### Step 1: Convert the owl's distance and time
1. **Owl's distance**: \( 8_{3}^{1} \)
- This is in base 3. To convert it to decimal:
\[
8_{3}^{1} = 8 \times 3^1 + 0 \times 3^0 = 8 \times 3 = 24 \text{ miles}
\]
2. **Owl's time**: \( { }_{4}^{3} \)
- This is in base 4. To convert it to decimal:
\[
{ }_{4}^{3} = 3 \times 4^0 = 3 \text{ hours}
\]
### Step 2: Convert the seagull's distance and time
1. **Seagull's distance**: \( 12_{2}^{1} \)
- This is in base 2. To convert it to decimal:
\[
12_{2}^{1} = 1 \times 2^1 + 2 \times 2^0 = 2 + 2 = 4 \text{ miles}
\]
2. **Seagull's time**: \( { }_{3}^{2} \)
- This is in base 3. To convert it to decimal:
\[
{ }_{3}^{2} = 2 \times 3^0 = 2 \text{ hours}
\]
### Step 3: Complete the statement
Now we can complete the statement:
- It takes the seagull **2 hours** to travel a **4 miles** distance.
So the completed statement is:
**It takes the seagull 2 hours to travel a 4 miles distance.**
Quick Answer
It takes the seagull 2 hours to travel 4 miles.
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