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Driving to Dallas

 
 
Reply Sun 30 Oct, 2005 05:02 pm
This is really a very simple problem, but many people find it deeply counter-intuitive.

You are driving by car to a particular destination, and our only assumption is that you are free to drive at any speed you choose - no traffic jams or anything like that. For the first half of the journey (i.e.half the distance) you drive at 20 miles per hour. You then realise that this is all taking much too long, and that you are going to be late. You therefore decide that you will increase your speed so that your overall average speed for the whole journey will be 40 miles per hour. How fast do you have to drive for the remaining part of your journey in order for your average speed for the whole journey to be 40 miles per hour?
 
View Profile markr
 
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Reply Sun 30 Oct, 2005 11:13 pm
infinitely fast
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View Profile Piffka
 
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Reply Sun 30 Oct, 2005 11:16 pm
Sixty miles an hour.
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Reply Mon 31 Oct, 2005 04:25 am
markr is quite close to the correct answer
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Reply Mon 31 Oct, 2005 06:03 am
Let's say the destination is 200 miles away.If you want to average 40mph you then take 5 hours.If after 100 miles at 20mph you have taken 5 hours you have no time left for the other 100 miles so the last 100 miles has to be instantaeneous.
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Reply Mon 31 Oct, 2005 04:08 pm
One of the things that people find difficult is that you have not specified the distance, but in fact the answer is the same, whatever the distance. The answer is that there is no answer - there is no speed you can drive at that will make your average speed 40 miles per hour. The reason is that to make your average speed for the whole journey 40 miles per hour, you need to be at your destination NOW, and no speed will allow you to achieve this.

How does this come about? Well, suppose you started out at 2 o'clock, and your destination is exactly 40 miles away. For your average speed to be 40 miles per hour, you need to arrive at 3 o'clock. But you drove the first half of the journey, 20 miles in this case, at 20 miles per hour. Which has taken you an hour. So it is now 3 o'clock, and you have only covered half the distance. There is no speed that you can drive for the second half of the journey that will make the average speed 40 miles per hour, since you need to be at your destination at this moment. And this applies no matter what the distance of the journey. If you prefer, you can change everything to kilometres per hour, instead of miles per hour.
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View Profile Chai
 
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Reply Mon 31 Oct, 2005 04:15 pm
There is no way you can drive to Dallas without hitting traffic.
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Reply Mon 31 Oct, 2005 06:20 pm
Feminine wisdom beats masculine logic every day of the week.
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View Profile Foxfyre
 
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Reply Sat 5 Nov, 2005 08:41 pm
Not to mention the logic of wanting to drive to Dallas in the first place.
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Reply Sun 6 Nov, 2005 08:13 am
Come to think of it ...I don't think I've ever driven to Dallas. I have driven from Dallas, having landed at the DFW airport. Just put it all behind me. Fort Worth and the country beyond is more fun than Big D anyway. I spent two weeks in Dallas one week-end.
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Reply Sun 6 Nov, 2005 08:18 am
Been there, done that. I would not drive to Dallas again if my life depended on it. Case closed! Laughing
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View Profile Jonsey
 
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Reply Sun 6 Nov, 2005 03:01 pm
I actually spent time in Dallas for business for a while. I had fun when friends were in town. Some of the museums were nice as well. Actually, I recently found a good news/info blog for Dallas - Webpage Title.

But you're right about traffic. I always remember traffic around the DFW/Dallas area.
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View Profile Foxfyre
 
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Reply Sun 6 Nov, 2005 03:51 pm
Jonsey wrote:
I actually spent time in Dallas for business for a while. I had fun when friends were in town. Some of the museums were nice as well. Actually, I recently found a good news/info blog for Dallas - Webpage Title.

But you're right about traffic. I always remember traffic around the DFW/Dallas area.


My husband and I drove to Dallas just last weekend in a driving rain and hail storm in a rental car whose windshield wipers didn't work properly. Its harder to decide what was most terrifying: the storm, the faulty wipers, the people so terrified they were driving at 5 mph and those who didn't seem to notice it was raining and were going their usual 80 or 90 mph. Then we spent three fascinating - not - hours at Love Field waiting for our plane to get around all the storms to get there from Houston.

Now none of this was Dallas's fault of course. But it sure illustrated why I don't want to drive there. Smile
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Reply Sun 6 Nov, 2005 05:22 pm
Did you get to meet Joanie?
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View Profile Foxfyre
 
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Reply Sun 6 Nov, 2005 05:34 pm
I don't know. I think I met everybody at Love Field that day.
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Reply Sun 6 Nov, 2005 06:38 pm
I'm just back from the pub Foxy but I've enough sense to resist that one.
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View Profile Foxfyre
 
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Reply Sun 6 Nov, 2005 06:45 pm
LOL. Well that's the name of the airport. Smile
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