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)Responses6 1124 hours6 1124 hours5 12 hours 5 12 hours5 1124 hours

1 answer

To find out how long you all spent driving, we need to convert the driving times into a consistent format (specifically, hours).

  1. Your driving time: 56 of an hour is equal to 56 minutes. To convert this into hours, we divide by 60:

    \[ \frac{56}{60} = \frac{14}{15} \text{ hours} \]

  2. Friend 1's driving time: 2 18 hours means 2 hours and 18 minutes. We convert the 18 minutes to hours:

    \[ 18 \text{ minutes} = \frac{18}{60} = \frac{3}{10} \text{ hours} \] So, Friend 1 drove for: \[ 2 + \frac{3}{10} = 2.3 \text{ hours} \]

  3. Friend 2's driving time: 3 12 hours means 3 hours and 12 minutes. We convert the 12 minutes to hours:

    \[ 12 \text{ minutes} = \frac{12}{60} = \frac{1}{5} \text{ hours} \] So, Friend 2 drove for: \[ 3 + \frac{1}{5} = 3.2 \text{ hours} \]

Now, we can add all the driving times together:

\[ \text{Total driving time} = \frac{14}{15} + 2.3 + 3.2 \]

First, let's convert \( 2.3 \) and \( 3.2 \) into fractions for easier addition:

\[ 2.3 = \frac{23}{10}, \quad 3.2 = \frac{32}{10} \]

Now, we will find a common denominator to add these values. The least common multiple of 15 and 10 is 30.

Converting everything to have a denominator of 30:

\[ \frac{14}{15} = \frac{28}{30}, \quad \frac{23}{10} = \frac{69}{30}, \quad \frac{32}{10} = \frac{96}{30} \]

Adding these together:

\[ \text{Total driving time} = \frac{28}{30} + \frac{69}{30} + \frac{96}{30} \]

Combine the numerators:

\[ \frac{28 + 69 + 96}{30} = \frac{193}{30} \]

To convert this to hours and minutes, we divide to find how many whole hours and what's left:

\[ 193 \div 30 = 6 \text{ R } 13 \]

This means there are 6 whole hours and \( \frac{13}{30} \) of an hour remaining. To convert \( \frac{13}{30} \) to minutes:

\[ \frac{13}{30} \times 60 = 26 \text{ minutes} \]

Thus, the total driving time for you and your friends was:

\[ \underline{6 \text{ hours and } 26 \text{ minutes}} \]

Since the options presented were more specific, the closest match is:

6 1/2 hours or approximately 6.43 hours.

Therefore, the correct answer is:

6 1124 hours (interpreted as 6 hours and 26 minutes).