Real-Life Math
You are a render wrangler who is overseeing the rendering for a new animated television show. The show will be a half-hour program that will air later this year.
The actual show requires 22.43 minutes of animation. It may not sound like many minutes, but the number of frames needed to fill this time slot is approximately 1,256,220.
Some of the frames take only a short amount of time to be rendered. Others take much longer. In movies such as Toy Story 2, some of the frames took three days before rendering was complete. You're not expecting anything that long, however, as the animations being used for this show are not as sophisticated as what was used in Toy Story 2.
During your shift, it is your job to ensure that each frame is rendered properly. It is also your responsibility to ensure that the computer system runs smoothly and that there are no glitches. If there are any errors, or if the computer system kicks out any renders, you must make sure you catch the error and fix it right away.
You begin your shift at 3 p.m. and work through until 11 p.m. During this time, several frames will go through the rendering process. At 11 p.m., the next render wrangler will take over and will work until 7 a.m. Then the next person will take over and work from 7 a.m. until 3 p.m., when your shift will start again.
Once the project is completed, all 1,256, 220 frames will have been rendered. If the time to render each frame has been logged, your department will know exactly how long the rendering took to complete. This is how the breakdown of times might look:
100,000 frames took 30 seconds to render
275,000 frames took 60 seconds to render
356,000 frames took 75 seconds to render
400,220 frames took 90 seconds to render
125,000 frames took 125 seconds to render
Assuming this is the correct breakdown of times, and that the render farm has 200 computers all processing frames at the same time, how many hours would it take to render the entire half-hour animated program?