Answer :
We start by converting the given times into minutes after midnight.
1. The filling starts at 10:52, which is calculated as:
[tex]$$
10 \times 60 + 52 = 600 + 52 = 652 \text{ minutes}.
$$[/tex]
2. The pool is half full at 13:14, which is calculated as:
[tex]$$
13 \times 60 + 14 = 780 + 14 = 794 \text{ minutes}.
$$[/tex]
3. The number of minutes required to fill the pool half full is:
[tex]$$
794 - 652 = 142 \text{ minutes}.
$$[/tex]
Since the pool fills at a constant rate, the time taken to fill it completely is twice the half-full time. Therefore, the total filling time is:
[tex]$$
2 \times 142 = 284 \text{ minutes}.
$$[/tex]
4. To find the time when the pool is completely full, add the total filling time to the start time:
[tex]$$
652 + 284 = 936 \text{ minutes after midnight}.
$$[/tex]
5. Finally, convert [tex]$936$[/tex] minutes back to hours and minutes. Dividing by [tex]$60$[/tex]:
[tex]$$
936 \div 60 = 15 \text{ with a remainder of } 36.
$$[/tex]
This gives a time of [tex]$15:36$[/tex] in the 24-hour clock format.
Thus, the swimming pool was completely full at
[tex]$$
\boxed{15:36}.
$$[/tex]
1. The filling starts at 10:52, which is calculated as:
[tex]$$
10 \times 60 + 52 = 600 + 52 = 652 \text{ minutes}.
$$[/tex]
2. The pool is half full at 13:14, which is calculated as:
[tex]$$
13 \times 60 + 14 = 780 + 14 = 794 \text{ minutes}.
$$[/tex]
3. The number of minutes required to fill the pool half full is:
[tex]$$
794 - 652 = 142 \text{ minutes}.
$$[/tex]
Since the pool fills at a constant rate, the time taken to fill it completely is twice the half-full time. Therefore, the total filling time is:
[tex]$$
2 \times 142 = 284 \text{ minutes}.
$$[/tex]
4. To find the time when the pool is completely full, add the total filling time to the start time:
[tex]$$
652 + 284 = 936 \text{ minutes after midnight}.
$$[/tex]
5. Finally, convert [tex]$936$[/tex] minutes back to hours and minutes. Dividing by [tex]$60$[/tex]:
[tex]$$
936 \div 60 = 15 \text{ with a remainder of } 36.
$$[/tex]
This gives a time of [tex]$15:36$[/tex] in the 24-hour clock format.
Thus, the swimming pool was completely full at
[tex]$$
\boxed{15:36}.
$$[/tex]