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A car departs at 8:15 AM and travels 195 km at an average speed of 105 km/h. If the driver takes a 20-minute coffee break, what time will they arrive?

Mathematics

ScanSolve AI Answer

Answer

10:26\text{10:26}

Step-by-step solution

4 steps
  1. Calculate the driving time.

    The driving time is calculated using the formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}.

    Driving time=195 km105 km/h=137 hours\text{Driving time} = \frac{195 \text{ km}}{105 \text{ km/h}} = \frac{13}{7} \text{ hours}
  2. Convert the driving time to hours and minutes.

    137 hours=1 hour+67 hours\frac{13}{7} \text{ hours} = 1 \text{ hour} + \frac{6}{7} \text{ hours}

    To convert the fractional part of an hour to minutes:

    67 hours×60 minutes/hour=3607 minutes≈51.43 minutes\frac{6}{7} \text{ hours} \times 60 \text{ minutes/hour} = \frac{360}{7} \text{ minutes} \approx 51.43 \text{ minutes}

    Rounding to the nearest minute, the driving time is 1 hour and 51 minutes.

  3. Calculate the total travel duration.

    The total travel duration includes the driving time and the coffee break.

    Total duration=Driving time+Coffee break\text{Total duration} = \text{Driving time} + \text{Coffee break} Total duration=1 hour 51 minutes+20 minutes\text{Total duration} = 1 \text{ hour } 51 \text{ minutes} + 20 \text{ minutes} Total duration=1 hour 71 minutes\text{Total duration} = 1 \text{ hour } 71 \text{ minutes}

    Since 71 minutes is 1 hour and 11 minutes:

    Total duration=1 hour+1 hour 11 minutes=2 hours 11 minutes\text{Total duration} = 1 \text{ hour} + 1 \text{ hour } 11 \text{ minutes} = 2 \text{ hours } 11 \text{ minutes}
  4. Determine the arrival time.

    The arrival time is the departure time plus the total travel duration.

    Arrival time=Departure time+Total duration\text{Arrival time} = \text{Departure time} + \text{Total duration} Arrival time=08:15+2 hours 11 minutes\text{Arrival time} = 08:15 + 2 \text{ hours } 11 \text{ minutes} Arrival time=10:26\text{Arrival time} = \text{10:26}

    The arrival time in Kokstad is 10:26.

    10:26\text{10:26}
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