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

1 answer

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.