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# Speeding up

159 replies to this topic

### #41 unreality

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Posted 12 July 2007 - 04:52 PM

lmao we know its impossible, but ther was no time limit, and no specifications that say you MUST travel on that road... you could take a longer route to reach the average of 60
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### #42 aniketkno

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Posted 15 July 2007 - 04:19 AM

I am so confused!!
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### #43 Incognitum

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Posted 15 July 2007 - 11:48 PM

You do in fact have to travel at the speed of light to get the average speed.

This in fact is not true. There is no substantive difference in this case between traveling 60,000km/h and traveling 1,079,252,848.8km/h. You must travel instantaneously to achieve the average without detouring.

If you really must work it out yourself the hard way (like I did :/) here is the math

6000km/h
30 / 6000 = 0.005
0.005x60 = 0.3 (this number means it took you 0.3 minute to travel 30km)
60/0.3=200 **
200
200x30=6000
6000+6000=12000
12000/201=59.7km/h average speed

Trying to figure this out was really hard.

The math is written out in the first few pages of the thread, no need to re-invent the wheel. To explain it simply: to get the average speed of 60km/h you must travel 60km in 1h. If you travel for that 1h and only go 30km you cannot. It is still possible to scale the average, and travel 120km in 2h. So having spent 1h to go 30km, you can now travel 90 km in the next 1h. This requires you to go 60 km further then you wanted to, which is why we are calling it the 'detour' solution.
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### #44 unreality

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Posted 15 July 2007 - 11:49 PM

exactly. i dont know why people cant think outside of the box and accept two solutions!
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### #45 rookie1ja

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Posted 16 July 2007 - 12:38 AM

just 2 points:
1st - I have never written that "You do in fact have to travel at the speed of light to get the average speed." as quoted above by Incognitum
2nd - due to original wording of the riddle, there are 2 answers - impossible or detour

no need to argue about that
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### #46 Incognitum

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Posted 16 July 2007 - 01:02 AM

just 2 points:
1st - I have never written that "You do in fact have to travel at the speed of light to get the average speed." as quoted above by Incognitum

You are correct sir, I apologize. When SirLogiC wrote his post, he quoted you, and while trying to edit my quote from him, I accidentally erased the wrong set of quote codes. My quotes aforementioned were both from SirLogic, thanks for catching that.

Here is his quote in more expansive format.

even traveling at 60,000km/h for that last 30km the average speed still only reaches 59.97km/h. One thing people arent realising is that as you travel that last 30km faster you travel for less time. If you travel that last time for 60km/h you arent traveling for 1 hour but 30km. That puts your average speed to 40km/h. You do in fact have to travel at the speed of light to get the average speed.

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### #47 PDR

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Posted 22 July 2007 - 04:28 PM

2nd - due to original wording of the riddle, there are 2 answers - impossible or detour

To expand on the "detour" concept - nothing in the problem statement said you had to drive straight there. If you drive for 1 hour at 30 km/hr, then another hour at 90 km/hr - you've now driven 2 hours for 120km total. As long as you now end up at town exactly at the 2 hour mark you've averaged 60km/hr over the entire trip.

An example of how this may make sense is if the town is on the other side of a mountain pass - lot's of switch backs etc. so that the road is not a straight line. The town is 60km from the starting point (as the crow flies), but the driving distance is longer (nothing in the problem statement said otherwise). Of course driving at 90km/hr on a winding road in a mountain pass is perhaps unwise, but again, nothing in the problem statement precludes that.

And finally, there are many other answers - assuming you accept the detour concept. What if you drive for 2 more hours at 75 km/hr. Now you've driven the original hour at 30km, plus 2 hours at 75 km (150km) for a total of 180km. This time it took a total of 3 hours - so 180km / 3 hours = 60km/hr. Thus there are an infinite number of answers - assuming you accept detour/winding roads as acceptable to the problem.
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### #48 JW15

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Posted 23 July 2007 - 09:13 PM

2nd - due to original wording of the riddle, there are 2 answers - impossible or detour

To expand on the "detour" concept - nothing in the problem statement said you had to drive straight there. If you drive for 1 hour at 30 km/hr, then another hour at 90 km/hr - you've now driven 2 hours for 120km total. As long as you now end up at town exactly at the 2 hour mark you've averaged 60km/hr over the entire trip.

An example of how this may make sense is if the town is on the other side of a mountain pass - lot's of switch backs etc. so that the road is not a straight line. The town is 60km from the starting point (as the crow flies), but the driving distance is longer (nothing in the problem statement said otherwise). Of course driving at 90km/hr on a winding road in a mountain pass is perhaps unwise, but again, nothing in the problem statement precludes that.

And finally, there are many other answers - assuming you accept the detour concept. What if you drive for 2 more hours at 75 km/hr. Now you've driven the original hour at 30km, plus 2 hours at 75 km (150km) for a total of 180km. This time it took a total of 3 hours - so 180km / 3 hours = 60km/hr. Thus there are an infinite number of answers - assuming you accept detour/winding roads as acceptable to the problem.

Agreed. Also, another easy way of seeing this as possible would be to imagine that after the first 30 km of travel you forgot something at home. You now need to return home (30 km back) and then the full distance to the town again (60 km) for a total of 120 km. If you can accomplish this inconvenient route in exactly 2 hours you have met the 60 km/hour desired average and still only technically travelled to a town 60 km away (it just took you 120 km total to do it). To accomplish this the "rest of the way" (back to home then onward to original destination) needs to be spent driving 90 km/hr as stated in previous posts.
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### #49 Incognitum

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Posted 24 July 2007 - 09:39 AM

Agreed. Also, another easy way of seeing this as possible would be to imagine that after the first 30 km of travel you forgot something at home. You now need to return home (30 km back) and then the full distance to the town again (60 km) for a total of 120 km. If you can accomplish this inconvenient route in exactly 2 hours you have met the 60 km/hour desired average and still only technically travelled to a town 60 km away (it just took you 120 km total to do it). To accomplish this the "rest of the way" (back to home then onward to original destination) needs to be spent driving 90 km/hr as stated in previous posts.

Presumably you need some time to slow down to turn around to go back to your house, and some more time still to get whatever you left there. This will require the actual driving parts of the trip to be faster in order to meet your 2 hr. time limit.
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### #50 Slick_Rick9009

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Posted 26 July 2007 - 09:54 AM

Simple explanation: Basically, it is asking how you can get there in an hour. average 60 kph with a distance of 60 km = an hour of travel time. You travel 30 km in an HOUR. It is now too late to make up time. The hour is over. Hopefully, that clears up confusion.

You know what the problem is... No where in the question does it say that you have only 1 hour to complete the task. People are missing the fact that "figuring that out" is the main part of the answer. You know you only have 1 hour because it says "YOU TRAVELED HALF WAY" Half way of 60 is 30 and you are traveling at 30 PER HOUR, so if your total distance at that point is 30kh it MUST HAVE TAKEN 1 hour to do it. Now that your HOUR is used up, Even if you traveled at 4 billion miles an hour, you can not change the fact that your Hourly Rate of Travel "WAS" 30Km per hour.... s***, Now I'm confusing myself... My head hurts. . . . . . I need a drink.lol

You may havee confused yourself but everyone else was confusing me till I read yours. Thanks. I got that Your average was 30km/h but I couldn't get past that. But, it's ok, I got it.
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