159 replies to this topic

[Martini]

MARTINI said if it takes you 80 min. to travel 60 km. then your AVERAGE speed is 45km/h. NO it is not AVERAGE speed. 45kmh is just the exact speed that you traveled the 60km and it took a duration of 80 min., as I said before. Also those numbers do not factor in both speeds, you think it does but look carefully because it doesn't. The reason why is because you have to do the formula twice (since there are two different speeds) to get the average.

EXAMPLE: If I traveled 30 km at 30kmh. Then traveled 30 km again at 90 kmh. What do you think my AVERAGE speed will be for the ENTIRE trip?????
30 kmh + 90 kmh = 120 kmh : 120 kmh / 2 (since two different speeds where used) = 60 kmh FOR THE ENTIRE DISTANCE of 60km.

These formulas Calculate SPEED, TIME and DISTANCE : SPEED = Distance / Time
TIME = Distance / Speed
DISTANCE = Speed x Time
They DO NOT calculate an AVERAGE.

Yes, they do:

http://www.onlinemat...d-problems.html (note the part that says "Be careful!" after the answer is given and then watch the video)

http://mathforum.org...view/53251.html

http://www.batesvill...s/AveSpeed.html

http://www.worsleysc...e/velocity.html

http://www.machinehe..._time_calc.html

http://www.glenbrook...DKin/U1L1d.html

[Seiai]

For reasons that I'm not going to get into right now, I'm going to revise my answer.

You would have to speed up infinitely fast in order to average 60 km/hr.


Which IRL might not be practical, but meh.

[Scraff]

MARTINI said if it takes you 80 min. to travel 60 km. then your AVERAGE speed is 45km/h. NO it is not AVERAGE speed. 45kmh is just the exact speed that you traveled the 60km and it took a duration of 80 min., as I said before. Also those numbers do not factor in both speeds, you think it does but look carefully because it doesn't. The reason why is because you have to do the formula twice (since there are two different speeds) to get the average.

Martini asked you to respond to his posts so he could get somewhere explaining why you're wrong. You're ignoring this simple request and repeating what doesn't make sense. He asked what you believe 45 km/hour is an exact speed of. Why repeat that again without answering the question?

So I'll repeat the question. If the first half of the trip was at 30 km/hour and the second half at 90 km/hour, what is 45 km/hour the exact speed of? That speed is an average speed for the trip.

EXAMPLE: If I traveled 30 km at 30kmh. Then traveled 30 km again at 90 kmh. What do you think my AVERAGE speed will be for the ENTIRE trip?????
30 kmh + 90 kmh = 120 kmh : 120 kmh / 2 (since two different speeds where used) = 60 kmh FOR THE ENTIRE DISTANCE of 60km.

These formulas Calculate SPEED, TIME and DISTANCE : SPEED = Distance / Time
TIME = Distance / Speed
DISTANCE = Speed x Time
They DO NOT calculate an AVERAGE.

Then what speed do they calculate? Please, read the links in Martini's last post!

You see you are misinterpreting what AVERAGE is. To get the average speed for the riddle you would have to calculate it this way. IT'S LIKE FOLLOWING AN ORDER OF OPERATION.

First Half of trip you traveled 30 km at a rate of 30kmh. Second half of the trip you traveled 30 km at a rate of 90 kmh. The average speed between 90kmh and 30kmh is 60kmh!

So, if you travel for 59 minutes at 70 mph and 1 minute at 10 mph, your average speed for the trip was 40 mph? No, if you traveled at an average speed of 40 mph for an hour's long journey, then you only drove 40 miles. Since you drove 70 mph for 59 minutes, you obviously drove a lot longer.

IF YOU WANTED TO SEE...

Please don't write in all caps. It only makes reading annoying and it doesn't help your case.

AND TO SEIAI, I DON'T KNOW WHO YOU ARE BUT WOW, YOUR MATHEMATICAL SKILLS AND PROBLEM SOLVING METHODS ARE AMAZING.

Then maybe his last post will convince you. By the way, someone agreeing with you about simple math doesn't make his methods AMAZING.

For reasons that I'm not going to get into right now, I'm going to revise my answer.

The reasons have been explained many times; no need to get into them.

You would have to speed up infinitely fast in order to average 60 km/hr.


Which IRL might not be practical, but meh.

Forget practical. It's not possible.

[Dirty Jed]

Speeding up - Back to the Logic Puzzles
If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?

There can actually be another answer. If you take "halfway" to mean half of the time, this changes the problem. Then it is 30k/h for 30minutes and then 90k/h for the last 30 minutes to cover 60k in one hour. (15k in the first 30 minutes and 45k in the last 30 minutes). It could be worded as: If I traveled half the distance to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the distance to have an average speed of 60 km/hour over the entire trip?

[Scraff]

There can actually be another answer. If you take "halfway" to mean half of the time, this changes the problem.

Of course it would change the problem, but the way the riddle is written it makes no sense to assume halfway to mean half the time. When one says they are half way to a destination, and they are going by time, they are estimating how long it would take to finish the trip. In your example you purposely have to go three times as fast. In the riddle, halfway obviously means half the distance. In the 16 pages this riddle has been discussed, not one person assumed that halfway meant anything but half the distance.

[MrAccident]

There is a solution - you need to get there immediately;-)

[Legion]

So, after reading a lot of posts I agree you must instantly arrive. The puzzle defines the terms and shy of breaking them we cant change the situation, one town is in a strait line with one road 60Km from the other. To average 60km/h you must travel 60km in one hour, thus defining the question to a one hour time limit since traveling at that rate would get you to the town in 1 hour exactly. No matter what the speed increase is you have already spent your 1 hour at 30km/h to get half way to the town. There's no time for travel so even with infinite speed the fastest average you could ever get is 59.999...1-8km/h as you can never get to .999 as we all know .999 repeating = 1. So the end answer is no you cannot reach the destination at 60km/h unless you instantly travel to the city.

[DaneBD]

You desire an average speed of 60 km/hr, but you've already spent a full hour going half-way. Sorry, but there is no speed possible to arrive in the next moment, which is your due time for 60 km/hr. The only decision you could make now is how late you can be; e.g.-at 120 km/hr, you would be 15 minutes late.

[Nebula Prophet]

The answer is not impossible, but rather infinite. If you continue at an infinitely large speed, you will reach your destination at (VERY!!) close to zero seconds - almost instantly. So small that it won't have an effect on the final average speed for the trip.

Spoiler for Impossible

I guess the answer is impossible - no such thing as 'infinite speed'....

[Quag]

bah this is a silly thread, but im bored
ok NP to to use the infinite speed thing it would only work if you accelrated at infinite m/s2 or else the time it takes you to get to the infinite speed will already make it slower than 60km/h now that kind of acceleration will instantly pankake well pretty much anything so you would arrive a corpse, of course there wouldnt even be a coprse left but you get my drift. only teleportation could make this work.

Edited by Quag, 05 May 2011 - 05:23 PM.