Answer
Two movies will start at the same time again after:
$2300$ minutes or $38$ hours and $20$ minutes after.
Work Step by Step
To know when the two movies will start again at the same time after noontime, one must use the least common multiple (LCM).
Since there is a 15-minute break between shows, find the LCM of:
$85 + 15 = 100$ minutes
and
$100 +15 = 115$ minutes
Factor each number completely :
$100 = 10(10) = 2(5) \cdot (2)(5) = 2(2)(5)(5)=2^2\cdot 5^2
\\115 = 5(23)$
Thus, the LCM is $2^2 \cdot 5^2 \cdot 23=2300$ minutes.
$2300$ minutes is $38$ hours and $20$ minutes.
Thus, the two movies will start at the same time $2300$ minutes or $38$ hours and $20$ minutes after.
