Speeding up

[Guest]

Finally, Xspyder, a voice of sanity. I think they all are still hunting the "extra dollar" from the old riddle.

Most certainly you can average 60 km/hr in the given parameters. Elementary

[Guest]

Where does it say you only have 2 hour? You can average 60 mph for 10 hours right? There is no reason why you can not drive faster for 1 more hour and have an average of 60mph. Maybe I am reading it wrong.

That's exactly what I was thinking! Also, everyone seems to think that the first part of the trip was only one hour. Going 30 km/hour for 60 km would take you TWO hours, not one. Also, there was no time limit to how fast the driver would get there as stated in the quote above. Therefore, I believe there is some sort of complicated solution (that I will be working on)

[Guest]

I stopped reading all the pages of up 4 when complete idiocy took the field over, much like a brawl at a soccer game,

or maybe an election, none are listening to the issues and most have lost the point. "Elduderino2085" has/had it correct

perhaps though he too was infected with the chaotic spell cast amongst the hurried crowd. Read ja's lips, exactly 60 miles, and not an inch more, thus defining parameters of the statement and the outcome of the answer. NO TIME LIMIT is mentioned and therefore there is exactly no time limit, not one second more nor less. Several had the answer there

within the first several pages of complete mayhem with the squares and roots and times all agagle over nought. It is 30 for the first half and then 90 for the second half distance equalling an average of 60 Km / hour, and not 60 km/ within an hour. "How I love thee, how I love thee.....Brain Den Maestros. Hey, I haven't had my Martini yet. What a beauuutifulll thing is the round table, oh and sweet the medecine that salves the spirit, yes it is so to think not in parrallel

with horse blinders on, though many could have been bridled with such, and perhaps some wax for the ears also. I'm sure more than several stable horse won the race laughing as most went careening into and off of the quide rails. RSVP

I just read this. and though it sounds so simple, I don't believe that is correct.

My simple explination to explain why i believe this way goes as so:

30 km for the first hour (at 30 km/h)

30 km for the second hour (at 30 km/h)

60 hm for 1/3 hours (40 min) (at 90 km/h)

30km+30km+60km=120km

1h+1h+.6666h=2.6666h

120km/2.6666h= 45km/h (rounded off)

[Guest]

NO TIME LIMIT is mentioned and therefore there is exactly no time limit, not one second more nor less.

There is a time limit.

"If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?"

If the town is 60 km away and you want to average 60 km per hour for the trip, then you must complete the trip in an hour. That's a time limit.

It is 30 for the first half and then 90 for the second half distance equalling an average of 60 Km / hour, and not 60 km/ within an hour.

Travel 30 km/hour for 30 km, and you've taken an hour. Travel 90 km/hour for 30 km, and you've taken 20 minutes. 60 km in 80 minutes is an average of 45 km/hour.

"How I love thee, how I love thee.....Brain Den Maestros. Hey, I haven't had my Martini yet.

Enjoy.

Also, everyone seems to think that the first part of the trip was only one hour. Going 30 km/hour for 60 km would take you TWO hours, not one.

The first part of the trip is 30 km, not 60 km. Where the riddle states "If I go halfway to the town (which is 60 km away)" 60km is how far away the town is from the starting point, not how far away half way to the town is from the starting point.

However, even if you misread the riddle and concluded that halfway to town is 60 km, you run in to the same problem. If the town is 120 km away and you want to average 60 km/hour for the entire trip, then you must complete the trip in two hours. If you spent two hours chugging along at 30 km/hour to get halfway to town, the only way to average 60 km per hour for the entire trip is to move at the speed of light for the remaining 60 miles. Since traveling at the speed of light causes time to stop moving from your point of view, the last 60 miles goes by in zero time. To an outside observer, it takes you a time of 60 miles/c to get there, which is nonzero. But if you're looking out for Number One, you can ignore other frames of reference. So the total time to go 60 miles is 2 hours, and the total time to go 120 miles is also 2 hours.

The only problem with this is you have to be massless. This makes a lot of other things in life problematic.

[Guest]

If the town is 60 km away and you want to average 60 km per hour for the trip, then you must complete the trip in an hour. That's a time limit.

...

The only problem with this is you have to be massless. This makes a lot of other things in life problematic.

Well said. I was stumped by this problem in a book when I was a kid, but I liked it because the answer made so much sense and seemed so simple. I was pleased when I ran across it on the forums. I'm surprised that there's so much debate over this. It somehow became far more complicated than it should have been. It has already been explained well enough by rookie1ja, Martini, and others, but I'll throw in my observation, for what it's worth.

The misunderstanding seems to result from the incorrect assumption that if you travel distance X at speed A, and then distance X at speed B, that your average speed is (A+B)/2. This fails to take into account that speeds A and B are rates which represent the ratio of distance to time (30 km/1 hr = ¹/₂60 km/1 hr). If you are going to add them together to arrive at an average, the time portions have to be the same. It's just like adding any fractions:

A/B + C/B = (A+C)/B (true)

What the naysayers are inadvertently suggesting by saying that ((30 km at 30km/hr) + (30km at 90km/hr))/2 = 60km/hr is:

A/B + C/BD = (A+C)/B

It's very easy to overlook this interaction between time and distance. That's what makes this such a great problem.

[Mekal]

s=speed t=time d=distance

first half

t 1h

d 30km

s 30km/h

second half

t 1/3h

d 30km

s 90km

advridge speed =60km

[rookie1ja]

s=speed t=time d=distance

first half

t 1h

d 30km

s 30km/h

second half

t 1/3h

d 30km

s 90km

advridge speed =60km

as per your data, total average speed should be total distance/total time ... so 60km/1.3333h ... which is 45km/h ... which is not the requested 60 km/h

[Guest]

s=speed t=time d=distance

first half

t 1h

d 30km

s 30km/h

second half

t 1/3h

d 30km

s 90km

advridge speed =60km

Mekal, you took the average of 30 and 90, but you ignored the times that you have provided. If you travel for a total of 80 minutes and only go 60km, you couldn't possibly have averaged 60km/hour, could you? To average 60km/hour over a distance of 60km, the only way you can do this is by taking one hour.

[Guest]

Beam me around Scotty, I need to teleport!

[Guest]

i think that this is really confusing , however, i do believe that there is a way to figure this out if you have the correct math.

the first answer that comes to mind is 90 kph, but this is not the correct choice because by the time one has reached 60 kph, the town is long gone.

while you could say it is impossible, or say take a detour, i think that there is math that you can do in order to find the answer

we know that there are 30 km left and the average must be 60 kph. it's only a matter of finding the correct answer and then stating how much time it would take to reach 60 kph - which would also be reaching the amount of time it takes to reach the town.

however, that is as far as my math would take me; i couldn't find the correct equation(s) in order to find a solution

maybe it really is impossible or a detour is necessary, OR the correct equation using the correct variables has not been found.

[Guest]

Let me see if I'm understanding things correctly. If I traveled half the distance(30 km) at 30kph theres no way to average 60 kph over the entire 60 km distance because 30kph is a frame of time and my times up? So I can never travel at a speed greater than the distance from point A to B in less than an hour?

Lets say your traveling to a town 60 km away. The only way to get to that town would to be at a speed less than 60kph. Because, according to what I'm reading, if you want to go to that same town at 90kph you would over shoot the town by 30 km because its impossible to travel at 90 kph unless you actually travel 90 km in an hour. If you don't travel for atleast 1 hour its impossible to travel at any speed because ,after all kph ,is a time frame not a rate of speed. So if i get to town in 45 minutes and stop and I didnt actually travel 90 kph. How fast did I go?

[Guest]

Let me see if I'm understanding things correctly. If I traveled half the distance(30 km) at 30kph theres no way to average 60 kph over the entire 60 km distance because 30kph is a frame of time and my times up?

30kph is a speed, not a time. The reason you can't average 60 kph over the entire 60 km distance is because in order to do that, the entire trip must take place in the time frame of exactly one hour. If one already spent one hour getting half way to the destination, finishing the trip must logically take more than one hour.

So I can never travel at a speed greater than the distance from point A to B in less than an hour?

No matter how fast you go, you can't get to your destination in an hour or less because you've already traveled for an hour.

Lets say your traveling to a town 60 km away. The only way to get to that town would to be at a speed less than 60kph. Because, according to what I'm reading, if you want to go to that same town at 90kph you would over shoot the town by 30 km because its impossible to travel at 90 kph unless you actually travel 90 km in an hour.

I'm not sure what you're misinterpreting, but there is nothing about overshooting the town given as a rationale for why one can't average a speed 60 km/hour for the entire trip.

So if i get to town in 45 minutes and stop and I didnt actually travel 90 kph. How fast did I go?

You're asking how fast you've gone if you traveled 60 km in 45 minutes? You've traveled at an average speed of 80 km/hour.

[Guest]

ok, so after reading a ton of replies, i have seen that we are going around and around in circles.

.__________.__________.

start middle end

total distance is 60km

from the start to the middle we traveled at 30km/h

because we know that half the total distance is 30km/h we know we travelled for 1 hour

If, like many people suggested we travelled at 90km/h then. . . .

we travelled at 90km/h for 30km

this means we travelled for 20 min, or 1/3 hour

if we add the two average speeds together (90 and 30) and divide by the time taken we get

120/1.3 does not = 60km

For the second half of the trip, the faster we go, the amount of time it takes to reach the destination is decreased.

For 90km/h to work, we would have to travel for 1 hour for each half of the trip. This isnt possible becasue we know that each half is 30km.

you cannot travel at a speed that would allow you average speed to be 60km/h

x X x

[Guest]

The normal answer is you can not because time has elapsed, but truthfully the answer is "infinite speed"

Speeding up - Back to the Logic Puzzles

If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?

Edit: "rest of the way" means to the town and not an inch farther and the total distance traveled has to be exactly 60 km (this is just to explain how I meant the riddle to be understood)

Speeding up - solution

This one has no solution. Unless we are complicating it with relativity theory - time and space. But to keep it simple, you can't reach the desired average speed under the given circumstances.

However, there is another option for the original wording - a detour. Think about that <!-- s;) --><!-- s;) -->

[Guest]

If you travel 30 kph for an hour and then you travel 90 kph for an hour what is the average kph? My math dictates that the average is 60 kph. I'm still having trouble seeing where thats wrong. It doesn't matter that it took two hours. Nothing in the question says it took an hour.

A radar gun for example doesnt know how long you been driving it only knows how fast your going in relation to a specific period of time. If your clocked at 90 kph thats how fast your going at that specific moment and has nothing to do with how long you've been driving.

Truck drivers use to theorize that they have a right to do the posted speed limit regardless of how fast they have to go to do it. If the speed limit is 90kph that means you have the right to go 90km in one hour. If your forced to slow down going up a steep hill or even stop for some reason you have then have the right to go what ever speed is nescessary to make up the remaining 90 km distance in that one hour.

KPH is an equation to judge relative speed at any specific time and in no way indicates an ACTUAL amount of time.

If i drive my car at 90 kph for 30 minutes I averaged a rate of speed of 90 kph the entire trip. If i do the same thing for 2 hours I have averaged a rate of speed 90 kph. If the question specifies an amount of time "1 hour" then that changes everything. The question did not pose a time limit.

I don't mean anything remotely derogatory by asking this but who the hell is MARTINI.

[Guest]

If you travel 30 kph for an hour and then you travel 90 kph for an hour what is the average kph? My math dictates that the average is 60 kph. I'm still having trouble seeing where thats wrong.

What's wrong is that you must include how long you drove at each speed before you get your average. In the case you gave above, you don't have to include the times because they are the same, so you can just give the average of 30 and 90. But what if you drove 100 kmh for twelve days and then drove 2 kph for 1 minute? You don't think you only averaged 51 kph, do you?

From post #104 by Martini:

"Travel 30 km/hour for 30 km, and you've taken an hour. Travel 90 km/hour for 30 km, and you've taken 20 minutes. 60 km in 80 minutes is an average of 45 km/hour."

Do you think that's wrong?

Nothing in the question says it took an hour.

For about the 100th time, yes, the question does say that the trip must take an hour, it just doesn't say it directly; you have to figure it out for yourself:

"If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?"

If you want to travel at an average of 60 kph for a total distance of 60 k, guess how long the trip will take? That's right- it takes 1 hour. Which means if you take longer than an hour, you can't average 60 kph- which means if you took one hour to get half way to your destination, you can't finish the trip in an hour without breaking the laws of physics.

Truck drivers use to theorize that they have a right to do the posted speed limit regardless of how fast they have to go to do it. If the speed limit is 90kph that means you have the right to go 90km in one hour.

Uh, this has nothing to do with the this thread, but what truck drivers where were ever dumb enough to have that theory? If the speed limit is 90kph, that does not mean you can travel faster than that if you plan on driving for at least an hour but plan on slowing down so that in an hour's time you didn't travel more than 90km. That notion is ludicrous.

I don't mean anything remotely derogatory by asking this but who the hell is MARTINI.

Why are you asking "who the hell" Martini is? He's a poster and a moderator who explained the correct answer to you. Who else is he supposed to be? Did he offend you? I'm not seeing it.

[Guest]

'm sorry you are wrong....

In order to reach the place at an average speed of 60 km/hour you would need to be able to teleport instantaneously to the place 60 km from the start because you already spent one hour at 30 km just to reach halfway.

Not quite:

Average speed is defined by distance, not the amount of time spent at that speed, since speed is a rate based on time. You take your weighted averages based on the distance...

Therefore your equation will be:

30 km/h * 30km/60km + X km/h * 30/60 = 60 km/h

X = 120 km/h

You travel 120 km/h for 0.25 h, and your average speed for the trip is 60km/h

[Guest]

You travel 120 km/h for 0.25 h, and your average speed for the trip is 60km/h

Wow! If you travel 120 km/h for 0.25 h your average speed is 120 km/h. It doesn't matter how long you drive, if you are traveling at 120 km/h, your average is 120 km/h. Where on Earth did you get 60km/h?

[Guest]

I meant traveling 120km/h for 0.25 hr, in which you travel the additional 30km to the end of the trip...

The 120km/h is the second half of the trip.

30km/h * 1hr + 120km/h * 0.25 hr = 60km (the total distance of the trip as stated)

30 km/h * 30km/60km + 120 km/h * 30/60 = 60 km/h (average speed, based of distance traveled).

[Guest]

Okay, I see what you're saying now. Let's see if your math works. You say if you travel 120km/h for 0.25 hr you will average 60 km/hour, right?

In the riddle you have driven 30 km/hour for one hour. If you then travel at 120 km/h for .25 hrs, you have driven 60 km in 1.25 hrs. This is average of 48 km/h. Read all of the posts and you'll see that the trip must be completed in an hour if the goal is to drive 60 km at an average speed of 60 km/hour. If you already took one hour to travel only half way to your destination, you can't average 60 km/hour.

[Guest]

Okay, I see what you're saying now. Let's see if your math works. You say if you travel 120km/h for 0.25 hr you will average 60 km/hour, right?

In the riddle you have driven 30 km/hour for one hour. If you then travel at 120 km/h for .25 hrs, you have driven 60 km in 1.25 hrs. This is average of 48 km/h. Read all of the posts and you'll see that the trip must be completed in an hour if the goal is to drive 60 km at an average speed of 60 km/hour. If you already took one hour to travel only half way to your destination, you can't average 60 km/hour.

The original problem statement does not state you need to complete the trip in an hour, only that you must travel no further than 60km.

How long you take should have no effect on the average. If you looked at my post above, you would see that I pointed out that the average should be taken according to distance covered at that speed, not at the time spent at that speed.

[Guest]

The original problem statement does not state you need to complete the trip in an hour, only that you must travel no further than 60km.

"If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?"

Above is the original problem. It states that the entire trip is 60 km and that you want your average speed for the trip to be 60 km/hour. Do you agree that the trip must then be completed in 1 hour?

If I tell you I want to drive 10 k and I want to average 20 km/hour, do you not think you can tell me exactly how long it will take to complete the 10 k?

How long you take should have no effect on the average.

That is incorrect.

Speed = distance / time

Time = distance / speed

Distance = time x speed

You need at least two of the above factors to calculate the third. The riddle states that you want to travel 60 km at an average of 60 km/hour. So how long will the trip take to accomplish that goal?

(time)x = (distance)60km ÷ (speed)60 km/hour

60÷60=1

The trip must be completed in one hour if the trip is 60 km and your goal is to average 60 km/hour.

If you looked at my post above, you would see that I pointed out that the average should be taken according to distance covered at that speed, not at the time spent at that speed.

So, you're still claiming that if you travel at 120 km/hour for the second half of the trip, you will have averaged 60 km/hour for the entire trip?

Let's take this one step at a time, please answer all the questions:

Do you agree that in the riddle the first half of the trip (which is 30 km) took one hour to complete since the driver traveled 30 km/hour? If no, please explain. if yes:

Now, your solution is to drive the second half of the trip (another 30 km away) at 120 km/hour. You already correctly stated that this would take .25 hour.

Do you agree that we can concluded that the entire trip took 1.25 hours? If no, please explain. If yes:

Do you agree that a trip that spanned 60 km and took 1.25 hours to complete means that the average speed for the trip was 48 km/hour (60 km÷1.25 hours = 48 km/hour)? If no, please explain.

[Guest]

"If I go halfway to the town (which is 60 km away) at the speed of 30 km/hour, how fast do I have to go for the rest of the way to have the average speed of the entire way 60 km/hour?"

Above is the original problem. It states that the entire trip is 60 km and that you want to average the trip at a speed at an average of 60 km/hour. Do you agree that the trip must then be completed in 1 hour?

If I tell you I want to drive 10 k and I want to average 20 km/hour, do you not think you can tell me exactly how long it will take to complete the 10 k?

That is incorrect.

Speed = distance / time

Time = distance / speed

Distance = time x speed

You need at least two of the above factors to calculate the third. The riddle states that you want to travel 60 km at an average of 60 km/hour. So how long will the trip take to accomplish that goal?

(time)x = (distance)60km * (speed)60 km/hour

60÷60=1

The trip must be completed in one hour if the trip is 60 km and your goal is to average 60 km/hour.

So, you're still claiming that if you travel at 120 km/hour for the second half of the trip, you will have averaged 60 km/hour for the entire trip?

Let's take this one step at a time, please answer all the questions:

Do you agree that in the riddle the first half of the trip (which is 30 km) took one hour to complete since the driver traveled 30 km/hour? If no, please explain. if yes:

Now, your solution is to drive the second half of the trip (another 30 km away) at 120 km/hour. You already correctly stated that this would take .25 hour.

Do you agree that we can concluded that the entire trip took 1.25 hours? If no, please explain. If yes:

Do you agree that a trip that spanned 60 km and took 1.25 hours to complete means that the average speed for the trip was 48 km/hour (60 km÷1.25 hours = 48 km/hour)? If no, please explain.

lol scraff that basically sum's it up and is pretty hard to argue with however...

for the more argumentative out there. You've got a lot of explaining to do

Edited April 14, 2008 by andreay

[bonanova]

If you travel 30 kph for an hour and then you travel 90 kph for an hour what is the average kph?

My math dictates that the average is 60 kph.

I don't mean anything remotely derogatory by asking this but who the hell is MARTINI.

Here's a friendly tip my friend ... two, actually.

[1] First, calculate how much time elapses if you make the trip averaging 60kph. Then think a bit.

[2] If you want to know who a member is, send a PM and introduce yourself. Politely. You'll likely get a pleasant response.

Now I'll introduce myself.

I'm bonanova.

I'm here to do what I can to make participation on this site an enjoyable experience for everyone.

I'm sure you get what I mean.

OK?

[Guest]

I don't know how you possibly took my question as derogatory. I premised the question by saying I didn't mean it to be IN ANY WAY OFFENSIVE. Sorry I didn't add a smiley face our add lol.

So if Martini found asking "who the hell he was" offensive I apologize to him/or her. Anybody else is obviously LOOKING for something to get uppity about and I'm not real concerned.

[2] If you want to know who a member is, send a PM and introduce yourself. Politely. You'll likely get a pleasant response.

Now I'll introduce myself.

I'm bonanova.

I'm here to do what I can to make participation on this site an enjoyable experience for everyone.

I'm sure you get what I mean.

OK?

Thank you. Whats a PM and how do you do it. My intent was not to be offensive. I was playing on a Bart Simpson quote.