# Answer to Riddle #89: Rate Determining Step

89. A manufacturing process for ceramics exists as described below:
Clay is sourced - unlimited supply.
The ceramics are shaped - takes about half an hour & there are 4 shapers.
They're painted - takes about half an hour (3 painters.)
Fired in a kiln - 300 at a time & takes 2 days.
Glazed - takes 15 minutes (2 glazers.)
Dried - takes a week but they have space to dry a lot, lets say 1000.
What is the maximum rate the ceramics can be produced?

I've been meaning to include a rate determining step based puzzle for a while and this is it:

The term 'rate determining step' comes from chemistry. Where in a complex reaction process series you can determine overall rate by just calculating the RDS.

So the 'trick' to solving these kind of problems is to work out the slowest part of the process and that is the rate determining step. No speeding up of any of the parts will help.

Activity Duration No. at a Time No. of People Effective Time
per Item
Shaped 0.5 1 4 0.1250
Painted 0.5 1 3 0.1667
Fired 48 300 1 0.1600
Glazed 0.25 1 2 0.1250
Air Dried 168 1000 1 0.1680

So I'm dividing the duration by the product of the number of people doing it and the number I can do at once to give me the effective duration, the time per item.

So despite my attempt at subterfuge the rate determining step is the last process, the drying. At a time of 0.168 hours or 10 minutes 4.8 seconds. 142.86 per day.

## Assumptions

This puzzle, unusually, exists in theory only. It involves lots of breaks from reality, not the least of which is that they are able work 24 hours a day. That it takes no time to load or empty the kiln...

Neither of the AI's got this answer right though Bard got the closest.

If you're curious what Bard made of this puzzle...

If you're curious what ChatGPT made of this puzzle...

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