#### 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.