Question
You and two other friends took turns driving during the trip. You each drove for the following amounts of time: 56
of an hour, 2 18
hours, and 3 12
hours. How long did you all spend driving?(2 points)
Responses
6 1124
hours
6 1124
hours
5 1124
hours
5 1124
hours
6 14
hours
6 14
hours
5 12
hours
of an hour, 2 18
hours, and 3 12
hours. How long did you all spend driving?(2 points)
Responses
6 1124
hours
6 1124
hours
5 1124
hours
5 1124
hours
6 14
hours
6 14
hours
5 12
hours
Answers
GPT-4o mini
To find the total driving time, we first need to add the times together. Let's convert the times to improper fractions for easier addition:
1. **First driver's time**:
- 56 minutes = \(\frac{56}{60}\) hours = \(\frac{14}{15}\) hours.
2. **Second driver's time**:
- \(2 \frac{1}{8}\) hours = \(\frac{17}{8}\) hours.
3. **Third driver's time**:
- \(3 \frac{1}{4}\) hours = \(\frac{13}{4}\) hours.
Now, let's add these times together:
\[
\text{Total time} = \frac{14}{15} + \frac{17}{8} + \frac{13}{4}
\]
To do this, we need a common denominator. The least common multiple (LCM) of 15, 8, and 4 is 120.
Now, we convert each fraction:
- \(\frac{14}{15} = \frac{14 \times 8}{15 \times 8} = \frac{112}{120}\)
- \(\frac{17}{8} = \frac{17 \times 15}{8 \times 15} = \frac{255}{120}\)
- \(\frac{13}{4} = \frac{13 \times 30}{4 \times 30} = \frac{390}{120}\)
Now, we add those fractions together:
\[
\frac{112}{120} + \frac{255}{120} + \frac{390}{120} = \frac{112 + 255 + 390}{120} = \frac{757}{120}
\]
Now, let's convert \(\frac{757}{120}\) into a mixed number:
- \(757 \div 120 = 6\) with a remainder of \(37\).
- So, \(\frac{757}{120} = 6 \frac{37}{120}\).
Now, we can convert \( \frac{37}{120} \) back into minutes:
- \( \frac{37}{120} \times 60 = 18.5 \) minutes.
Therefore, the total time spent driving is:
\[
6 \text{ hours and } 18.5 \text{ minutes} \quad \text{(or } 6 \frac{1}{2} \text{ hours)}
\]
Given the responses:
- **6 1124 hours** (does not seem like a valid response)
- **5 1124 hours** (does not seem like a valid response)
- **6 14 hours** (seems like a typographical error—possibly meant to represent **6 1/4 hours**)
- **5 12 hours** (does not seem valid)
The closest correct formatted response, based on the proper time calculation, would most closely resemble **6 1/2 hours**, which was not listed. Assuming a typographical error in the responses, your total driving time is approximately **6 hours and 18.5 minutes.**
1. **First driver's time**:
- 56 minutes = \(\frac{56}{60}\) hours = \(\frac{14}{15}\) hours.
2. **Second driver's time**:
- \(2 \frac{1}{8}\) hours = \(\frac{17}{8}\) hours.
3. **Third driver's time**:
- \(3 \frac{1}{4}\) hours = \(\frac{13}{4}\) hours.
Now, let's add these times together:
\[
\text{Total time} = \frac{14}{15} + \frac{17}{8} + \frac{13}{4}
\]
To do this, we need a common denominator. The least common multiple (LCM) of 15, 8, and 4 is 120.
Now, we convert each fraction:
- \(\frac{14}{15} = \frac{14 \times 8}{15 \times 8} = \frac{112}{120}\)
- \(\frac{17}{8} = \frac{17 \times 15}{8 \times 15} = \frac{255}{120}\)
- \(\frac{13}{4} = \frac{13 \times 30}{4 \times 30} = \frac{390}{120}\)
Now, we add those fractions together:
\[
\frac{112}{120} + \frac{255}{120} + \frac{390}{120} = \frac{112 + 255 + 390}{120} = \frac{757}{120}
\]
Now, let's convert \(\frac{757}{120}\) into a mixed number:
- \(757 \div 120 = 6\) with a remainder of \(37\).
- So, \(\frac{757}{120} = 6 \frac{37}{120}\).
Now, we can convert \( \frac{37}{120} \) back into minutes:
- \( \frac{37}{120} \times 60 = 18.5 \) minutes.
Therefore, the total time spent driving is:
\[
6 \text{ hours and } 18.5 \text{ minutes} \quad \text{(or } 6 \frac{1}{2} \text{ hours)}
\]
Given the responses:
- **6 1124 hours** (does not seem like a valid response)
- **5 1124 hours** (does not seem like a valid response)
- **6 14 hours** (seems like a typographical error—possibly meant to represent **6 1/4 hours**)
- **5 12 hours** (does not seem valid)
The closest correct formatted response, based on the proper time calculation, would most closely resemble **6 1/2 hours**, which was not listed. Assuming a typographical error in the responses, your total driving time is approximately **6 hours and 18.5 minutes.**