BrainDen.com - Brain Teasers

# Speeding up

## 160 posts in this topic

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

I don't understand how you differentiate distance and time. How does having traveled half way in space mean unequivocally that your hour is used up? Why not say you've traveled halfway in space and halfway in time, so you have two hours total? Why does the distance dictate the time at all? The whole point of speed is the relation between distance and time, when you arbitrarily state that one supercedes the other the question of variable speeds becomes irrelevant.

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For the people who believe this is possible I am sorry but you are wrong. You are looking at this from incorrect points of view. When you average speed you do not do it like averaging discrete numbers (i.e. 1,2,3... (whole numbers)). You divide the distance by the time it took to travel. Even if it took 0 seconds to travel the second half of the trip, your average speed would be (60 km)/(1 hr)= 60 km/hr. If you went 90 km/hr for the last 30 km it would take you 1/3 hr to reach town => the average would be 1.333 hrs (total time)/ 60 km (total distance) = 45 km/hr. To reach an average speed of 90 km/hr you would need to travel further.

Hope this helps explain.

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For the people who believe this is possible I am sorry but you are wrong. You are looking at this from incorrect points of view. When you average speed you do not do it like averaging discrete numbers (i.e. 1,2,3... (whole numbers)). You divide the distance by the time it took to travel. Even if it took 0 seconds to travel the second half of the trip, your average speed would be (60 km)/(1 hr)= 60 km/hr. If you went 90 km/hr for the last 30 km it would take you 1/3 hr to reach town => the average would be 1.333 hrs (total time)/ 60 km (total distance) = 45 km/hr. To reach an average speed of 90 km/hr you would need to travel further.

Hope this helps explain.

Thanks for the hot tip, however I feel my point of view is fine thanks. Perhaps next time try reading what we are saying before telling us we're wrong?

No one has been more swift then myself to correct those who think they've solved this puzzle by making an error in their arithmatic. However, your own post proposes a detour solution similar to the one we've been advocating.

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When solving logic problems there are certain assumptions you are supposed to make. In this problem one of the assumptions is that you travel to town on a path and when you get half way there you dont take a detour while traveling faster to make up for the time spent traveling slower. The question is assuming you continue traveling only for another 30 km. "If I go halfway to town...how fast do I have to go for the rest of the way". So if you only travel another 30 km you cannot reach the desired average speed for the trip.

Picking apart the wording of questions is possible on most of these logic problems but it is not their intention.

Also my post wasnt directed towards people who understand the concept of averaging speed of a trip but for those who were trying to average 2 numbers because you traveled the same distance but not take into account the time.

So in conclusion yes you can travel more than 30 km and reach the average speed but the real solution is that it is impossible because the question implies that the first 30km is halfway.

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When solving logic problems there are certain assumptions you are supposed to make.

Foremost among them that there is a solution for those who are clever enough.

If 'it's impossible' is an acceptable answer for logic puzzles they are no longer any fun.

Q:

1. How many gray whales does it take to change a lightbulb?

2. How many cows would it take to create a particle accelerator?

3. What is the average IQ score for pairs of pants that have completed 7th grade?

4. How long would it take to fly to the moon inside your #2 pencil?

5. When your electric shaver rampages through the city killing thousands, how often does it need to be plugged in to recharge?

A:

1. It's impossible; all whales use energy efficient fluorescent lights that come with lifetime guarantees.

2. It's impossible; everyone known the key ingredient in particle accelerators is pork!

3. It's Impossible; even pairs of pants with PhDs cannot lift a pencil to take an IQ test.

4. It's impossible; all #2 pencils require air for their engines to fire.

5. It's impossible; what, you have a killer robot razor?

Now, was that any fun at all?

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The difference between the speeding up question and the ones you posted is your first instinct in speeding up is figuring out what speed you have to travel then realising you cant do it. To me it was interesting because at first i was like thats easy..then theres the oh yeah I guess you cant do that. In your questions the assumption most people would or should make is that the situations you are talking about are not real and you are only looking for creative responses. To me speeding up is much more fun than the "think outside of the box" questions you posted.

But I guess to each his own.

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Hmm... you know, this looks possible.

Lets see.....

For the first part of the journey, he travelled 30km at a speed of 30 kmh.

Time in the inertial frame of reference: 1 hour

unknown time = Time with respect to observer in inertial frame of reference

sqrt[1-(30kmh^2/c^2)]

unknown time: 59999999999.999699584484865522271 nanoseconds

Which gives him 0.00030041551513447773 nanoseconds to cover 30 km

=0.0000000000000050069252522412955 hours to cover 30 km

=5991701191578769.8403966508288831 kmh

He only needs to travel at 5991701191578769.8403966508288831 kmh to average 60kmh. =)

Haha.

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The difference between the speeding up question and the ones you posted is your first instinct in speeding up is figuring out what speed you have to travel then realising you cant do it. To me it was interesting because at first i was like thats easy..then theres the oh yeah I guess you cant do that. In your questions the assumption most people would or should make is that the situations you are talking about are not real and you are only looking for creative responses. To me speeding up is much more fun than the "think outside of the box" questions you posted.

But I guess to each his own.

I was actually attempting to interject a little levity into the conversation, but I guess I'm the only one who thought it was funny.

Seriously though, I do feel as though returning the answer 'it's impossible' is a defeatist way to approach a logic puzzle, but we may have to agree to disagree here.

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There is nothing in the problem that says you have to go straight to town. You could do as the problem says, and travel 30km in one hour. Then take a detour and travel an additional hour at a rate of 90km per hour. Then you will have reached the town traveling a total of 120km in two hours, or an average of 60km per hour right?

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While there is nothing in the problem that states you have to travel directly to town there are many things that imply the question means you travel directly to town.

As far as the 2 answers go they are really the same answer. If you understand that you cant travel a distance of 30km in one hour and have your average speed be 60 km/hr after having traveled only 60 km then you understand the problem and that really is the main objective. However saying that people who say it is impossible are stupid and saying people who say it is possible if you dont travel straight to town are smart and creative thinkers does not make sense to me.

People who answered it is impossible say "it is impossible" and leave it at that. They understand that traveling off path would make it possible to reach a speed of 60 km/hr.

Do you really think saying you travel further is "thinking outside of the box", or do you think it is ignoring the assumptions the problem is trying to make you follow.

The reasons for the assumptions in my opinion are:

1. "If I go halfway to Town"-implies he is halfway there.

2. "to go the rest of the way"-because it says the way

3. "How fast do I have to go"-It is asking you for a speed, not for a speed and a distance.

While the 2 answers are correct the first answer is the simplest and in my opinion what they are looking for, at least the way they have worded this question.

You can pick apart almost any question if you spend enough time.

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If I have ever in my life claimed to be either smart or creative, I have certainly never claimed to be both at the same time.

These Logic problems/ riddles are full of loop holes. If these problems were simple and straight foward then the forums trying to answer them would not be so lengthy (7 pages for instance). Nor would they be as fun to read and take part in.

The intention of my answer was not to be "smart and creative" or to "think outside the box". I was just pointing out one of the many loop holes in this particular problem. The loop hole I gave was even hinted at in the author's solution, so I can't even claim it as my own.

I was also not calling anyone stupid, and to imply that I was is an unfair accusation. Frankly, everyone here is much smarter than I am. I agree that "impossible" is the most accurate answer to this problem. I just don't agree that it is the only possible answer. As you said, the two solutions are essentially the same thing.

Thanks for listening

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Not to get tons more posts but i never was saying "rubarb1" was calling people who said impossible un-creative and such but if you read previous people have said things like that and others.

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I read all the posts before replying. I understand that you weren't refering to just me, but I was included in the group you were refering to. I can't speak for the others, so I just spoke for myself. Sorry if it sounded too personal. Just throwing my two cents in that is all. No hard feelings.

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Impossible. One can do this only if He/She could stop time.....

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Star Trek anyone? Beam me up, Scotty!

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I know how the people who don't get the elaborative math language feel.

I'm only in middle school.?

but either way I think I can explain this problem at an easier level than some others.

the distance is 60 km

you want your average to be 60 km per hour

if you did that from the start you'd get there In 1 HOUR

thats where The time limit 1 hour came from.

but if u traveled @ 30 km per hour you've used up your 1 hour when u got half way there

thus even if u went at infinant speed u would never reach the average of 60 km

And for every one else I told my dad this one and he got it but then told me to make an equation for it

All I knew was the equation of D=R*T

60km= (30km)*(30km per hour)+(30km)*(t)

....(ignore these dots)........ 2

and I'm just a middle schooler that just learned D=R*T a few weeks ago!

and he joked that in order to reach 60km per hour u'd go !/@ of infinity

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where in the question does it say the whole journey must only take one hour?

if you do the first half at 30km per hour and the second half at 90km per hour then the average is 6okm/per hour over 2 hours

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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)

ok people just saying there is no time limit on the trip all it say is that it is 60 km away. No time at all just distance. And if u are taking a stright route there then its impossible to average 60km/h. Why?

because you would need to travel at 90 km/h for the next hour to average it out and u would pass the town.

starting point - - - - - -halfway traveling 30km/h - - - - - - town - - - - - - where u would end up if traveled at 90km/h to average it out

each - is equal to 5 km

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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)

60 km/hour means PER HOUR not IN ONE HOUR, but assuming that it meant 60km/hr in one hour...

Halfway would be 30 minutes, and you have driven 15 km. To get the rest of the way of 45km in 30 minutes you would need to drive 90km/hr which is a given speed.

You also don't need to travel for an hour to go a certain speed. If you go from your home to the corner store which is a mile away. Traveling at 60km/hr means you are going 60km/hr and it just means you will get to the corner store in 1 minute.

Now assuming that it meant 30km is halfway the answer does not change, because you don't need to travel the entire time at a given speed to have an average speed.

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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)

60 km/hour means PER HOUR not IN ONE HOUR, but assuming that it meant 60km/hr in one hour...

No need to make that assumption. The riddle is asking about 60 km per hour.

Halfway would be 30 minutes, and you have driven 15 km.

No. Half way would take 1 hour and you will have gone 30 km.

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In stating that you have gone 15km I was being facetious and assuming the trip was done in an hour. Halfway would indeed be 30km.

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Being facetious? You stated that halfway you would have driven 30 minutes and gone 15 km. This is incorrect, no being facetious about it.

The trip cannot be completed in an hour because in one hour you will have only gone 30km.

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My entire point must have been missed there, where do you get that the trip needs to be completed in an hour?

My be facetious was in saying halfway could also be contrused as a time frame as well as a distance. If there is this mysterious hour that the logic puzzle is based on... then thinking outside the box, halfway could be 30 minutes of said mysterious hour.

I have to re-terate the point of speed as well, per hour does not mean you can only get a speed if you travel for an hour. Because if that is true then I am going to "speed" all over town and tell the cop that pulls me over "I haven't been driving for an hour so I couldn't have been doing 180km/hr"

The point of a puzzle is the find the answer and not to say "it's impossible". That's just plain stupid. Kind of like saying "Without a time machine, how can you stop an already exploded bomb from exploding."

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My entire point must have been missed there, where do you get that the trip needs to be completed in an hour?

Right here:

"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 the trip must be completed in an hour.

My be facetious was in saying halfway could also be contrused as a time frame as well as a distance.

Right. The first half of the trip was done in 60 minutes and 30 km was traveled.

If there is this mysterious hour that the logic puzzle is based on... then thinking outside the box, halfway could be 30 minutes of said mysterious hour.

Right. But you said "Halfway would be 30 minutes, and you have driven 15 km." That's incorrect.

I have to re-terate the point of speed as well, per hour does not mean you can only get a speed if you travel for an hour. Because if that is true then I am going to "speed" all over town and tell the cop that pulls me over "I haven't been driving for an hour so I couldn't have been doing 180km/hr"

No one is saying you have to drive for an hour to go a certain speed.

The point of a puzzle is the find the answer and not to say "it's impossible". That's just plain stupid. Kind of like saying "Without a time machine, how can you stop an already exploded bomb from exploding."

It's not stupid. It's a good stumper and it seems to have stumped you. The point is that to many it seems possible and if the riddle stated from the beginning it can't be done, then it wouldn't be much of a riddle, would it?