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3. The table below shows tide data for a location on the north shore of Long Island, in New York State.

\begin{tabular}{|c|c|c|}
\hline
Day & Tide & Time \\
\hline
\multirow{4}{}{Tuesday} & High Tide & 12:11 a.m. \\
\cline {2-3} & Low Tide & 6:23 a.m. \\
\cline {2-3} & High Tide & 12:36 p.m. \\
\cline {2-3} & Low Tide & 6:49 p.m. \\
\hline
\multirow{3}{}{Wednesday} & High Tide & 1:02 a.m. \\
\cline {2-3} & Low Tide & 7:15 a.m. \\
\cline {2-3} & High Tide & 1:27 p.m. \\
\hline
\end{tabular}

Based on these data, what is the most likely time of the next high tide?

A) 1:53 a.m.

B) 1:53 p.m.

C) 7:40 a.m.

D) 7:40 p.m.



Answer :

GinnyAnswer
To determine the most likely time of the next high tide, we need to analyze the pattern of high tide intervals.

### Step-by-Step Solution:

1. Identify the intervals between the high tides:
- From Tuesday 12:11 a.m. to Tuesday 12:36 p.m.
- From Tuesday 12:36 p.m. to Wednesday 1:02 a.m.

2. Convert the high tide times to minutes past midnight for easy calculation:
- Tuesday 12:11 a.m. = 0 hours and 11 minutes = 11 minutes past midnight.
- Tuesday 12:36 p.m. = 12 hours and 36 minutes = 12 60 + 36 = 720 + 36 = 756 minutes past midnight.
- Wednesday 1:02 a.m. = 1 hour and 2 minutes = 1 60 + 2 = 60 + 2 = 62 minutes past midnight.

3. Calculate the differences between the consecutive high tide times:
- Difference between Tuesday 12:11 a.m. and Tuesday 12:36 p.m.:
[tex]\[ \text{Difference}_{\text{Tuesday}} = 756 \text{ minutes} - 11 \text{ minutes} = 745 \text{ minutes} \][/tex]
- Difference between Tuesday 12:36 p.m. and Wednesday 1:02 a.m.:
[tex]\[ \text{Difference}_{\text{Wed}} = 62 \text{ minutes} + 1440 \text{ minutes} (for over midnight) - 756 \text{ minutes} = 62 + 1440 - 756 = 746 \text{ minutes} \][/tex]

4. Calculate the average interval between high tides:
[tex]\[ \text{Average difference} = \frac{745 \text{ minutes} + 746 \text{ minutes}}{2} = \frac{1491 \text{ minutes}}{2} = 745.5 \text{ minutes} \][/tex]

5. Predict the next high tide time by adding the average interval to the last known high tide (Wednesday 1:02 a.m.):
- Convert 1:02 a.m. back to minutes past midnight:
[tex]\[ 1:02 \text{ a.m.} = 62 \text{ minutes} \][/tex]
- Add the average interval:
[tex]\[ \text{Next high tide in minutes} = 62 \text{ minutes} + 745.5 \text{ minutes} = 807.5 \text{ minutes} \][/tex]

6. Convert 807.5 minutes back to the standard time format:
- Divide 807.5 minutes into hours and remaining minutes:
[tex]\[ 807.5 \text{ minutes} = 13 \text{ hours and } 27.5 \text{ minutes} \][/tex]
- 13 hours corresponds to 1:27 p.m. when converting to a 12-hour format.

Given the possible answers:
A) 1:53 a.m.
B) 1:53 p.m.
C) 7:40 a.m.
D) 7:40 p.m.

The most likely time of the next high tide corresponds to the time we calculated, which is around 1:27 p.m. The closest provided answer is:

B) 1:53 p.m.