High School

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An empty swimming pool is filled at a constant rate.

Filling started at 11:54 and the pool was half full at 14:16.

At what time was the swimming pool completely full? Give your answer using the 24 hour clock.

Answer :

To solve this problem, we need to determine how long it takes to fill the entire pool once we know it was half full at 14:16.

  1. Calculate the time taken to fill the pool halfway:

    • Filling started at 11:54, and the pool was half full at 14:16.
    • First, find the difference between these two times.

    [tex]14:16 - 11:54[/tex]

    • Convert these times into minutes to find the difference:

    [tex](14 \times 60 + 16) - (11 \times 60 + 54) \\
    = (840 + 16) - (660 + 54) \\
    = 856 - 714 = 142 \text{ minutes}[/tex]

  2. Determine the time to completely fill the pool:

    • Since the pool was half full in 142 minutes, it will take another 142 minutes to fill the remaining half of the pool.
    • Therefore, the total time to fill the entire pool will be [tex]142 \times 2 = 284[/tex] minutes from the start time.

  3. Find the time the pool will be completely full:

    • Start time was 11:54, and we add 284 minutes to this time.
    • Convert 284 minutes to hours and minutes:

    [tex]284 \text{ minutes} = 4 \text{ hours and } 44 \text{ minutes}[/tex]

    • Add this to the start time:

    [tex]11:54 \text{ plus } 4 \text{ hours and } 44 \text{ minutes} \\
    = 16:38[/tex]

Therefore, the swimming pool will be completely full at 16:38 (4:38 PM) when using a 24-hour clock.

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