Answer
$2$ minutes $18$ seconds
Work Step by Step
First, convert 3 minutes to seconds:
\[
3 \text{ minutes} = 3 \times 60 = 180 \text{ seconds}.
\]
Since she improves (reduces) her time by 3 seconds each day, we have an arithmetic sequence:
\[
T_n = T_0 - 3n,
\]
where \(T_0 = 180\) seconds (her time on day 0) and \(T_n\) is her time (in seconds) on day \(n\).
On day 14,
\[
T_{14} = 180 - 3 \times 14 = 180 - 42 = 138 \text{ seconds}.
\]
To convert back to minutes and seconds:
\[
138 \text{ seconds} = 2 \text{ minutes and } 18 \text{ seconds}.
\]
