Warrior General Games

40 mph, and I'm embarrassed I no longer remember how to do this easily.

Originally posted by Catullus16
guess which one is the science teacher -- http://glb.warriorgeneral.com/game/forum_thread.pl?thread_id=5260783

Originally posted by Catullus16
bob travels in exactly one direction for 10 miles at a steady rate for 20 minutes.
bob continues travelling in the same direction for another 10 miles at the steady rate of 60mph.

what is bob's average rate of speed for the entire trip?




the first line confuses me because you just said at a steady rate for the first one but did not give a speed

nevermind, dont even answer. idgaf.

i studied history. i either add to zero or subtract to zero

Originally posted by Darren Sanders



the first line confuses me because you just said at a steady rate for the first one but did not give a speed

Speed is just distance over time

Originally posted by Timmah
Speed is just distance over time

yeah but he said bob travels 10 miles at a steady rate for 20 minutes

thats ambiguous. it could be that he traveled part of the 10 miles at a steady rate for 20 minutes and then the rest of the time spent travelling was at lightspeed.

I think he meant bob travels 10 miles at a steady rate IN 20 minutes

Originally posted by Darren Sanders
yeah but he said bob travels 10 miles at a steady rate for 20 minutes

thats ambiguous. it could be that he traveled part of the 10 miles at a steady rate for 20 minutes and then the rest of the time spent travelling was at lightspeed.

I think he meant bob travels 10 miles at a steady rate IN 20 minutes

Doesn't matter because either way he only traveled 10 miles in a 20 minute span. He averaged 30 mph to do that. Which is irrelevant to figure out the answer. You get the answer, because overall bob traveled 20 miles in 30 minutes which would put him on pace for 40 miles in 60 minutes, aka 40 mph

Originally posted by Timmah
Doesn't matter because either way he only traveled 10 miles in a 20 minute span. He averaged 30 mph to do that. Which is irrelevant to figure out the answer. You get the answer, because overall bob traveled 20 miles in 30 minutes which would put him on pace for 40 miles in 60 minutes, aka 40 mph

im literally just nitpicking the wording of the question. Nowhere does it say that he traveled 10 miles in 20 minutes. It says he traveled

in one direction

for 10 miles

at a steady pace for 20 minutes

You see what I mean?

just because he was at a steady pace for 20 minutes does not mean that he travelled the ten miles in those 20 minutes

I understand

Originally posted by Timmah
40 mph, and I'm embarrassed I no longer remember how to do this easily.

yup, that's the correct answer.

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 what i said to spin at the very start -- the average rate is not necessarily the average of the rates. for this question, it would need to be 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 viola, 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 that intuitive to compute, they imply consecution and elide simultaneity, and often are completely meaningless -- like in the example that kicked this whole thing off. for example, consider someone asking how many widgets a factory can produce in an hour when what they really want to know is how many widgets a factory employee can produce in an hour. only by asking the latter can you account for the simultaneity and get at the true amount of time it takes to produce a widget.

Originally posted by Darren Sanders
yeah but he said bob travels 10 miles at a steady rate for 20 minutes
thats ambiguous. it could be that he traveled part of the 10 miles at a steady rate for 20 minutes and then the rest of the time spent travelling was at lightspeed.
I think he meant bob travels 10 miles at a steady rate IN 20 minutes

i can see why you consider it ambiguous, though that sort of notation is actually intended to be the opposite. direction, distance, rate, duration. the problem with "IN" is that it can imply any duration not greater than 20min.

^^^^^

That's what a buzzkill looks like.

Takes a simple joke about Redster's sister being a whore and tries to turn it into a math lesson that nobody needs, all because I happened to use the word "average" in my initial statement, when EVERYBODY else knew what I was talking about.

Originally posted by Darren Sanders
just because he was at a steady pace for 20 minutes does not mean that he travelled the ten miles in those 20 minutes

and here i went so far out of my way to make it clear that there was nothing tricky about the problem.

y'all are a suspicious bunch.

Originally posted by spindoctor02
^^^^^

That's what a buzzkill looks like.

Takes a simple joke about Redster's sister being a whore and tries to turn it into a math lesson that nobody needs, all because I happened to use the word "average" in my initial statement, when EVERYBODY else knew what I was talking about.

nope.

what really happened is that you said i was wrong, so it seemed like you wanted to discuss it. are we done?