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?
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:
Before reading the answer can I interest you in a clue?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...
© Nigel Coldwell 2004 - – The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please inquire using the link at the top of the page. Secure version of this page.
PayPal
I always think it's arrogant to add a donate button, but it has been requested. If I help you get a job though, you could buy me a pint! - nigel
