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A family traveled 126 miles. The trip took 2 hours and 40 minutes. What was their average speed in mph, rounded to the nearest mph?

Mathematics

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Question 3.1.1

  1. Convert the total travel time into hours.

    The family took 2 hours and 40 minutes.
    To convert minutes to hours, divide by 60:

    40 minutes=4060 hours=23 hours≈0.6667 hours40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours} \approx 0.6667 \text{ hours}

    Total time in hours:

    Time=2+23 hours=63+23 hours=83 hours\text{Time} = 2 + \frac{2}{3} \text{ hours} = \frac{6}{3} + \frac{2}{3} \text{ hours} = \frac{8}{3} \text{ hours}

  2. Use the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}.

    Given distance is 126 miles.

    Speed=126 miles83 hours\text{Speed} = \frac{126 \text{ miles}}{\frac{8}{3} \text{ hours}}

  3. Calculate the average speed.

    Speed=126×38 mph=3788 mph=47.25 mph\text{Speed} = 126 \times \frac{3}{8} \text{ mph} = \frac{378}{8} \text{ mph} = 47.25 \text{ mph}

  4. Round the average speed to the nearest mile per hour.

    47.25 mph≈47 mph47.25 \text{ mph} \approx 47 \text{ mph}

    The average speed for the trip was 47 mph\boxed{\text{47 mph}}.

    Question 3.1.2

  5. Identify the departure time and travel duration.

    Departure time: 09:15
    Travel duration: 2 hours and 40 minutes

  6. Add the hours component of the travel duration to the departure time.

    09:15+2 hours=11:1509:15 + 2 \text{ hours} = 11:15

  7. Add the minutes component of the travel duration to the current time.

    11:15+40 minutes11:15 + 40 \text{ minutes} 15 minutes+40 minutes=55 minutes15 \text{ minutes} + 40 \text{ minutes} = 55 \text{ minutes}

    So, the time becomes 11:5511:55.

    The family arrived in Harrison at 11:55\boxed{\text{11:55}}.

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