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Combine Operations
Join Date: May 2005
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Recuperator,
You are right. I did construe your bantering as a personal attack. However, I accept your apology, so let’s be friends and say no more about that. Did I say I was actually not a farmer, by the way?
But you are still wrong about the rest. Remember my warning – if the word “Average” is used, always smell a rat. Cap Loko saw the nail and hit it right on the head – the question suggests a number as an answer. If the question had been, “If you travel at a steady 40 km/hr from point A to point B, IS IT POSSIBLE TO TRAVEL AT SUCH A SPEED ON THE RETURN JOURNEY TO AVERAGE 80 KM/HR”, that might have made more people scratch their heads and say, “Now just hang on a minute, let’s think about this one.” The obvious answer is “Yes, of course. What a stupid question.” But then you might think, “Why should an intelligent person ask such a stupid question? Is it, after all, really such a stupid question?” And maybe a tiny seed of doubt is planted.
Recuperator, you fatal error is adding two average speeds and assuming the average of those speeds is actually the average overall speed. You cannot do this. It does not work. To find the average speed, you add up the total distance, and you divide it by the time it takes to cover that distance. Distance = speed x time.
As regards Formula 1 (and I missed yesterday’s race), if you are simply recording lap times, then yes, you time each lap, add up the times, and divide by the number of laps. This gives you the average lap time, but that is all. You cannot use this to work out the average speed, it just does not work that way, my friend.
To use your example in motor racing, one lap at 40 km/hr and one lap at 120 km/hr does not give you an average speed of 80 km/hr. Please believe me.
Let us say a lap is 120 km long. I know this is ridiculous, and even the old Nurburgring didn’t come close, but it is an easy number to use, and once again you can use any distance you wish:
Lap one: 120 km / 40 km/hr will take you 3 hours.
Lap two: 120 km / 120 km/hr will take you 1 hour.
Total distance: 240 km.
Total time: 4 hours.
AVERAGE speed: 240 km / 4 hours gives you 60 km/hr.
Another question for you: You have two groups of people; the average age of one group is 40 years, and the average age of the other group is 60 years. What is the average age of both groups? Let me warn you again – I have used the word “Average” here, three times. Smell a rat. I might even admit that this is a trick question
Another point: I suspect (and hope) that you have more than the average number of fingers and toes, I certainly do.
James ozzie, like I said before, a great question, which is still confusing a lot of people. Thank you for enlightening my on year 11, that’s something I’ve learnt.
Farmer.
You are right. I did construe your bantering as a personal attack. However, I accept your apology, so let’s be friends and say no more about that. Did I say I was actually not a farmer, by the way?
But you are still wrong about the rest. Remember my warning – if the word “Average” is used, always smell a rat. Cap Loko saw the nail and hit it right on the head – the question suggests a number as an answer. If the question had been, “If you travel at a steady 40 km/hr from point A to point B, IS IT POSSIBLE TO TRAVEL AT SUCH A SPEED ON THE RETURN JOURNEY TO AVERAGE 80 KM/HR”, that might have made more people scratch their heads and say, “Now just hang on a minute, let’s think about this one.” The obvious answer is “Yes, of course. What a stupid question.” But then you might think, “Why should an intelligent person ask such a stupid question? Is it, after all, really such a stupid question?” And maybe a tiny seed of doubt is planted.
Recuperator, you fatal error is adding two average speeds and assuming the average of those speeds is actually the average overall speed. You cannot do this. It does not work. To find the average speed, you add up the total distance, and you divide it by the time it takes to cover that distance. Distance = speed x time.
As regards Formula 1 (and I missed yesterday’s race), if you are simply recording lap times, then yes, you time each lap, add up the times, and divide by the number of laps. This gives you the average lap time, but that is all. You cannot use this to work out the average speed, it just does not work that way, my friend.
To use your example in motor racing, one lap at 40 km/hr and one lap at 120 km/hr does not give you an average speed of 80 km/hr. Please believe me.
Let us say a lap is 120 km long. I know this is ridiculous, and even the old Nurburgring didn’t come close, but it is an easy number to use, and once again you can use any distance you wish:
Lap one: 120 km / 40 km/hr will take you 3 hours.
Lap two: 120 km / 120 km/hr will take you 1 hour.
Total distance: 240 km.
Total time: 4 hours.
AVERAGE speed: 240 km / 4 hours gives you 60 km/hr.
Another question for you: You have two groups of people; the average age of one group is 40 years, and the average age of the other group is 60 years. What is the average age of both groups? Let me warn you again – I have used the word “Average” here, three times. Smell a rat. I might even admit that this is a trick question
Another point: I suspect (and hope) that you have more than the average number of fingers and toes, I certainly do.
James ozzie, like I said before, a great question, which is still confusing a lot of people. Thank you for enlightening my on year 11, that’s something I’ve learnt.
Farmer.
Thread Starter
Lets move on
As the initiator of this debate, I think it time we laid it to rest. Thanks for the many well reasoned replies. Can I offer a simple illustration, using the numbers?
Assume A to B 40 km & outbound leg always 40 km/hr (therefore always 60 minutes)
If you return at 120 km/hr, return time is 20 minutes, total time is 80 minutes over 80 km so average speed is 60km/hr
If you return at 1,200 km/hr return time is 2 minutes, total time is 62 minutes over 80km so average speed is 77.43km/hr
If you retrun at 12,000 km/hr, return time is 0.2 minutes, total time is 60.2 minutes so average speed is 79.73 km/hr
If you return at 120,000 km/hr, return time is 0.02 minutes, total time is 60.02 minutes so average speed is 79.97 km/hr
You get the drift...
Asymtotic on 80 km/hr (lovely buzz word)
I will post another elegant problem sometime.
Well done to those who saw the problem very early (Sultan, Farmer, Loka and others)
Assume A to B 40 km & outbound leg always 40 km/hr (therefore always 60 minutes)
If you return at 120 km/hr, return time is 20 minutes, total time is 80 minutes over 80 km so average speed is 60km/hr
If you return at 1,200 km/hr return time is 2 minutes, total time is 62 minutes over 80km so average speed is 77.43km/hr
If you retrun at 12,000 km/hr, return time is 0.2 minutes, total time is 60.2 minutes so average speed is 79.73 km/hr
If you return at 120,000 km/hr, return time is 0.02 minutes, total time is 60.02 minutes so average speed is 79.97 km/hr
You get the drift...
Asymtotic on 80 km/hr (lovely buzz word)
I will post another elegant problem sometime.
Well done to those who saw the problem very early (Sultan, Farmer, Loka and others)
Amen!
Join Date: Aug 2004
Location: Joeys
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Asymptotic? James Ozzie is a learned man. I had to go to dictionary.com to figure that out.
"A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve". Eesh
"A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve". Eesh
