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Eighteen pupils were given a playground to clear in 1h 40min. If six of the pupils did not turn up, how much longer did it take the rest of the pupils to clear the playground?

Mathematics

ScanSolve AI Answer

Answer

50 minutes\text{50 minutes}

Step-by-step solution

6 steps

: Pupils clearing a playground

  1. Convert the initial time to minutes.

    The original time for 18 pupils to clear the playground is 1 hour 40 minutes.

    1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes} 1 hour 40 minutes=60 minutes+40 minutes=100 minutes1 \text{ hour } 40 \text{ minutes} = 60 \text{ minutes} + 40 \text{ minutes} = 100 \text{ minutes}
  2. Calculate the total work required in "pupil-minutes".

    The total work is the product of the number of pupils and the time taken.

    Total work=18 pupils×100 minutes=1800 pupil-minutes\text{Total work} = 18 \text{ pupils} \times 100 \text{ minutes} = 1800 \text{ pupil-minutes}
  3. Determine the number of pupils who turned up.

    Six pupils did not turn up, so the number of pupils working is:

    Pupils working=18−6=12 pupils\text{Pupils working} = 18 - 6 = 12 \text{ pupils}
  4. Calculate the time taken by the remaining pupils.

    To complete the same amount of work with fewer pupils, the time taken will be:

    New time=Total workPupils working=1800 pupil-minutes12 pupils=150 minutes\text{New time} = \frac{\text{Total work}}{\text{Pupils working}} = \frac{1800 \text{ pupil-minutes}}{12 \text{ pupils}} = 150 \text{ minutes}
  5. Convert the new time to hours and minutes.

    150 minutes=15060 hours=2 hours and 30 minutes150 \text{ minutes} = \frac{150}{60} \text{ hours} = 2 \text{ hours and } 30 \text{ minutes}
  6. Calculate how much longer it took.

    The difference between the new time and the original time is:

    Difference=(2 hours 30 minutes)−(1 hour 40 minutes)\text{Difference} = (2 \text{ hours } 30 \text{ minutes}) - (1 \text{ hour } 40 \text{ minutes})

    To subtract, convert 2 hours 30 minutes to 1 hour 90 minutes:

    Difference=(1 hour 90 minutes)−(1 hour 40 minutes)=0 hours 50 minutes\text{Difference} = (1 \text{ hour } 90 \text{ minutes}) - (1 \text{ hour } 40 \text{ minutes}) = 0 \text{ hours } 50 \text{ minutes}

    The playground took 50 minutes longer to clear.

    Comparing this to the options provided, option A contains "50min".

    The final answer is 50 minutes\text{50 minutes}.

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