20miles/30min ~ 40mph
Forum > General Discussion > pick a speed, bob
Catullus16
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Originally posted by Venkman
40
yup, that's the correct answer.
from elsewhere:
Originally posted by Catullus16
the temptation is to say 10mi/20min=30mph and avg(30,60)=45, but that's answering an entirely different question. since we want the average for the entire trip, it's better to just start with totals -- the two legs are equal distance and the second one takes 10min, so we have 20mi/30min=40mph
the issue here is that the average rate is not necessarily the average of the rates. for this question, we need the weighted average of the rates, given that speed is distance/time and bob is spending unequal amounts of time at each rate. intuitively, we know his average rate will be closer to 30 because he spends more time at that speed -- twice as long, in fact, so we could take (2/3)30+(1/3)60 and voila, we get 40mph again.
the real takeaway is that average rates seem simple on the surface but can lead straight to several different pitfalls. they're not necessarily intuitive to compute, they imply consecution, can elide simultaneity, and often are completely meaningless. for example, consider someone trying to figure out how long it takes to make a widget by asking how many widgets a factory can produce in an hour. but since the employees are working simultaneously, they should instead be asking how many widgets a factory employee can produce in an hour. to get at duration, you need to ask the right average rate (or have some other term to account for simultaneity).
40
yup, that's the correct answer.
from elsewhere:
Originally posted by Catullus16
the temptation is to say 10mi/20min=30mph and avg(30,60)=45, but that's answering an entirely different question. since we want the average for the entire trip, it's better to just start with totals -- the two legs are equal distance and the second one takes 10min, so we have 20mi/30min=40mph
the issue here is that the average rate is not necessarily the average of the rates. for this question, we need the weighted average of the rates, given that speed is distance/time and bob is spending unequal amounts of time at each rate. intuitively, we know his average rate will be closer to 30 because he spends more time at that speed -- twice as long, in fact, so we could take (2/3)30+(1/3)60 and voila, we get 40mph again.
the real takeaway is that average rates seem simple on the surface but can lead straight to several different pitfalls. they're not necessarily intuitive to compute, they imply consecution, can elide simultaneity, and often are completely meaningless. for example, consider someone trying to figure out how long it takes to make a widget by asking how many widgets a factory can produce in an hour. but since the employees are working simultaneously, they should instead be asking how many widgets a factory employee can produce in an hour. to get at duration, you need to ask the right average rate (or have some other term to account for simultaneity).
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