Quote by pebbles
Something is wrong; I did 300 J/s * t (seconds to get 8.9X10^5 Joules)=8.9 X10^5 J
Divided both sides by 300 J and got 3.0 X 10^3 seconds; the answer is 3.7 X10^2 s.

The reason you are coming up short...
You also need to make similar calculation for heating the glass cup.
The sum (time to heat water + time to heat glass)
is the time it takes to raise the temperature 85 deg
glass cup, mass= 300g (given)
You should have a table in your text of specific heats for other materials or ask your teacher.
One online source gives specific heat of
glass = 0.84 J/(gm/deg K).