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Answer :
We start with an initial time of $7:45$ AM.
1. First, add the minutes. Adding $20$ minutes to the $45$ minutes gives:
$$
45 + 20 = 65 \text{ minutes.}
$$
Since $60$ minutes make an hour, $65$ minutes is equivalent to $1$ hour and $5$ minutes.
2. Now, add the hours. We originally add $3$ hours to the starting hour $7$, and we must also include the extra hour from the minute sum:
$$
7 + 3 + 1 = 11 \text{ hours.}
$$
3. The remaining minutes after converting $65$ minutes is $5$ minutes.
Putting it all together, the time $3$ hours and $20$ minutes after $7:45$ AM is:
$$
11:05 \text{ AM.}
$$
1. First, add the minutes. Adding $20$ minutes to the $45$ minutes gives:
$$
45 + 20 = 65 \text{ minutes.}
$$
Since $60$ minutes make an hour, $65$ minutes is equivalent to $1$ hour and $5$ minutes.
2. Now, add the hours. We originally add $3$ hours to the starting hour $7$, and we must also include the extra hour from the minute sum:
$$
7 + 3 + 1 = 11 \text{ hours.}
$$
3. The remaining minutes after converting $65$ minutes is $5$ minutes.
Putting it all together, the time $3$ hours and $20$ minutes after $7:45$ AM is:
$$
11:05 \text{ AM.}
$$
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