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Verify, showing ALL calculations, whether Mr Son left his home at exactly 11:40. The following formula may be used: Distance = average speed × time.

Mathematics

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Answer

not valid\text{not valid}

Step-by-step solution

5 steps

here's the solution to your question:

To verify whether Mr. Son left his home at exactly 11:40, we need to calculate the actual travel time and then subtract it from his arrival time.

  1. Use the given formula to calculate the time taken for the journey.

    The formula is: Distance = average speed ×\times time.
    We need to find the time, so we rearrange the formula:

    Time=DistanceAverage speed\text{Time} = \frac{\text{Distance}}{\text{Average speed}}
  2. Substitute the given values into the formula.

    Distance = 34 km
    Average speed = 85 km/hour

    Time=34 km85 km/hour\text{Time} = \frac{34 \text{ km}}{85 \text{ km/hour}} Time=0.4 hours\text{Time} = 0.4 \text{ hours}
  3. Convert the time from hours to minutes.

    Since there are 60 minutes in an hour:

    Time in minutes=0.4 hours×60 minutes/hour\text{Time in minutes} = 0.4 \text{ hours} \times 60 \text{ minutes/hour} Time in minutes=24 minutes\text{Time in minutes} = 24 \text{ minutes}
  4. Calculate the departure time by subtracting the travel time from the arrival time.

    Arrival time = 12:10
    Travel time = 24 minutes

    Departure time=12:10−24 minutes\text{Departure time} = 12:10 - 24 \text{ minutes}

    To subtract 24 minutes from 12:10, we can think of 12:10 as 11 hours and 70 minutes (since 1 hour = 60 minutes, 12:10 = 11:70).

    Departure time=11:70−00:24\text{Departure time} = 11:70 - 00:24 Departure time=11:46\text{Departure time} = 11:46
  5. Compare the calculated departure time with the statement.

    The calculated departure time is 11:46.
    The statement says Mr. Son left his home at exactly 11:40.
    Since 11:46≠11:4011:46 \neq 11:40, Mrs. Son's statement is not valid.

    Mr. Son’s statement is not valid\text{Mr. Son's statement is } \boxed{\text{not valid}}
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