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Hello John,
I would appreciate your assistance in solving this problem as specified in the subject:
The times taken to produce each of the first four batches of a new product were as follows:
Batch Number Time Taken
1 100 minutes
2 70 minutes
3 59 minutes
4 55 minutes,What was the rate of learning closest to?
A 85%
B 84.3%
C 78.6%
D 70%What I have done is the following:
Firstly I have determined total times for each as well as average times (y)Batch Number Time Taken Total Time Avg.time
1 100 minutes 100 min 100min
2 70 minutes 100+70=170min 170/2=85min or 100*r
3 59 minutes 170+59=229min 229/3=76,33min or 100*rˆ2
4 55 minutes, 229+55=284 284/4=71min or 100*rˆ3Looking at the row number 2 and its last column it suggests that r=85/100=85%, but I wanted to check and my assumption is that at batch 4, which is batch 2 doubled, y=71min=100*rˆ3. Therefore r=3rd?0,71 and I get 90% there.
So I tried also with the 3rd batch, although this one is not doubled just to give it a shot.
And I got y=76,33=100*rˆ2, so r=?0,7633=87%.The solutions state that the answer is under B, without giving any explanation.
Could you please explain me what would be the best way to do it, and what am I getting wrong here?
Many thanks!
RegardsMarko
What you have written for batches 1 and 2 is correct.
It is batches 3 and 4 where you are wrong.
The average time for 3 batches is indeed 76.33 minutes, but this does not equal 100 x r^2 (because we have not doubled).The average time for 4 batches is indeed 71 minutes, but this does not equal 100 x r^3
4 batches is doubling twice, and so 71 minutes is equal to 100 x r^2So r^2 = 71/100
So r = 0.843 or 84.3%As you said in your lecture, people make silly mistakes…
Thanks, this was an eye opener!
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