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A group of friends, Peter, Mary and John, went on a road trip. Peter arrived at his destination at 12:45 after travelling for 20 minutes. They left Thaba Nchu at the time shown on watch A, which is 12

Mathematics

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Step-by-step solution

16 steps
  1. Identify the type of watch.

    Watch A displays time using digits.

    The type of watch represented in A is a digital watch.

  2. Determine the arrival time from watch B.

    Watch B is an analog clock. The hour hand is between 12 and 1, and the minute hand is pointing at 9. This indicates 45 minutes past the hour.
    So, the arrival time is 12:45.

  3. Calculate the departure time.

    Peter arrived at 12:45 after travelling for 20 minutes. To find the departure time, subtract 20 minutes from the arrival time.

    12:45−20 minutes=12:2512:45 - 20 \text{ minutes} = 12:25
  4. Write the departure time in words.

    12:25 in words is twenty-five minutes past twelve.

  5. Determine the departure time.

    The group left Thaba Nchu at the time shown on watch A, which is 12:45.

  6. Calculate the total duration of stops.

    • Kimberley: 37 minutes
    • Engen garage: 1 hour = 60 minutes
    • Beaufort West: 10 minutes
    • Laingsburg: 35 minutes Total stop time:
    37+60+10+35=142 minutes37 + 60 + 10 + 35 = 142 \text{ minutes}

    Convert total stop time to hours and minutes:

    142 minutes=2 hours and 22 minutes(120 minutes=2 hours)142 \text{ minutes} = 2 \text{ hours and } 22 \text{ minutes} \quad (120 \text{ minutes} = 2 \text{ hours})
  7. Calculate the total travel time.

    Driving time: 11 hours
    Total stop time: 2 hours 22 minutes
    Total travel time:

    11 hours+2 hours 22 minutes=13 hours 22 minutes11 \text{ hours} + 2 \text{ hours } 22 \text{ minutes} = 13 \text{ hours } 22 \text{ minutes}
  8. Calculate the arrival time in Cape Town.

    Departure time: 12:45
    Add total travel time: 13 hours 22 minutes

    12:45+13 hours 22 minutes12:45 + 13 \text{ hours } 22 \text{ minutes}

    First, add the hours:

    12:45+13 hours=01:45 (the next day)12:45 + 13 \text{ hours} = 01:45 \text{ (the next day)}

    Then, add the minutes:

    01:45+22 minutes=02:0701:45 + 22 \text{ minutes} = 02:07

    The calculated arrival time is 02:07 (AM).

  9. Compare with the teacher's claim.

    The teacher claims they will arrive at 00:25.
    Our calculated arrival time is 02:07.
    Therefore, the teacher is incorrect.

  10. Determine the start time of the Math lit period.

    The period started at the time shown on watch A, which is 12:45.

  11. Calculate the end time of the Math lit period.

    Duration of the period: 45 minutes

    12:45+45 minutes=13:3012:45 + 45 \text{ minutes} = 13:30
  12. Calculate the start time of the next period.

    There is a 5-minute break after the period.

    13:30+5 minutes=13:3513:30 + 5 \text{ minutes} = 13:35
  13. Compare with Mr Matete's claim.

    Mr Matete stated the next period will start at 14:00.
    Our calculated start time for the next period is 13:35.
    Therefore, Mr Matete is incorrect.

  14. Determine Mr Nyamakazi's departure time.

    He departed on the time shown on watch A, which is 12:45.

  15. Calculate Mr Nyamakazi's arrival time in Botsabelo.

    Departure time: 12:45
    Travel duration: 34 minutes

    12:45+34 minutes12:45 + 34 \text{ minutes} 45 minutes+34 minutes=79 minutes45 \text{ minutes} + 34 \text{ minutes} = 79 \text{ minutes} 79 minutes=1 hour and 19 minutes79 \text{ minutes} = 1 \text{ hour and } 19 \text{ minutes}

    So, add 1 hour and 19 minutes to 12:00:

    12:00+1 hour 19 minutes=13:1912:00 + 1 \text{ hour } 19 \text{ minutes} = 13:19

    The calculated arrival time is 13:19.

  16. Compare with Mr Nyamakazi's claim.

    Mr Nyamakazi claimed he arrived at 13:12.
    Our calculated arrival time is 13:19.
    Therefore, Mr Nyamakazi is incorrect.

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