Speeding up

[Guest]

you guys are all wrong. The answer is 60 because it says how fast will you have to drive for THE REST OF THE WAY to be an average of 60. not the whole way.

[Guest]

you guys are all wrong. The answer is 60 because it says how fast will you have to drive for THE REST OF THE WAY to be an average of 60. not the whole way.

Here's a riddle for you: "If you've read half the question at 30 WPM, how much of the rest of the question do you need to read to understand what we are talking about?"

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?

[Guest]

I believe the answer is indeed 90km per hour. The question does not state that there is a limit placed on the amount of time one must take to get from one point to the other, which means all one must do is speed up in order to average 60km per hour overall. It does not state that one must travel between the two points within 1 hour. Perhaps the answer was meant to be something different, but as far I as I can tell the question was not phrased in such a way. So here is my logic in bullet form:

There are two points spaced 60km apart

You travel halfway at 30km/h

To average 60km/h you must travel at 90km/h to make up the initial sluggishness

Having done so, you have now traveled 60km and averaged 60km/h

This seems correct to me.

[Guest]

I believe the answer is indeed 90km per hour. The question does not state that there is a limit placed on the amount of time one must take to get from one point to the other, which means all one must do is speed up in order to average 60km per hour overall. It does not state that one must travel between the two points within 1 hour. Perhaps the answer was meant to be something different, but as far I as I can tell the question was not phrased in such a way. So here is my logic in bullet form:

There are two points spaced 60km apart

You travel halfway at 30km/h

To average 60km/h you must travel at 90km/h to make up the initial sluggishness

Having done so, you have now traveled 60km and averaged 60km/h

This seems correct to me.

Yeah, here is the part your not quite getting: the average is not calculated by speed over distance. Your model produces an average of 60(km/h)/km. The average we're looking for is calculated by distance over time(km/h). Because 90km/h is faster then 30km/h it takes less time to cover the distance remaining. So you are going slow for a long time, and fast for a short time. So you don't get to spend 30 minutes at 90mph to bring the average up if you are traveling in a straight line. To spend 30 minutes at 90km/h you must overshoot your mark by 15km. I hope that helps clear things up a little.

Maybe this will help illustrate the point: A kayak and a motor boat have a race up river two knots and back down to the starting place (total of 4 knots in the race). The motor boat travels at 2 knots per hour both directions, but the kayak travels at 1 knot per hour upstream, and 3 knots per hour downstream. Who wins the race?

[Guest]

A good brain teaser stretches your imagination and helps break the tendency to automatically think in mundane linear patterns.

I believe the intended solution to this puzzle is that it is not possible.

However the "wait a minute, who says you only have one hour." concept also qualifies ...especially if you consider it after recognizing the intended solution.

There is a difference between nitpicking over how well or poorly the question is written, and having fun considering the possible alternate solutions. Learning to recognize the intended solution despite possible flaws in the wording is an important skill. (And will help your grades)

[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?

The solution of not possible makes sense to me, and I understand the questions of the people above. I am going to try to answer those questions, but I'm bad at wording, so sorry if it doesn't help.

The question is asking for the average speed of the ENTIRE trip. Therefore, with a total distance of 120 km and an average speed of 60 km/hour, the average time you must take is 2 hours. Because you already took 2 hours to complete the first half, you are out of time.

Now the question is why can't you speed up to 120 km/hour for the second half and then average that to get 60 km/hour. Well, the thing is that when you average the two speeds to get the average speed for the entire trip, you come up with (30 + 120)/2=75 km/hour. As you can see, this is not 60 km/hour and does not satisfy the problem. You must be wondering why I didn't include the distances in that small equation. Well, it is asking for average SPEED, not average speed OVER A GIVEN DISTANCE. Because of that, you can only use the two speeds you went at to average 60.

I apologize for the last couple of sentences, because I kind of repeated myself. I hope that makes sense.

[Guest]

Now the question is why can't you speed up to 120 km/hour for the second half and then average that to get 60 km/hour. Well, the thing is that when you average the two speeds to get the average speed for the entire trip, you come up with (30 + 120)/2=75 km/hour. As you can see, this is not 60 km/hour and does not satisfy the problem. You must be wondering why I didn't include the distances in that small equation. Well, it is asking for average SPEED, not average speed OVER A GIVEN DISTANCE. Because of that, you can only use the two speeds you went at to average 60.

I don't agree with this statement for two reasons.

1. if you went an average of 75 km/hr and only traveled 60km, you would be there in less than an hour, which is imposible, because it took you an hour just to get halfway (going 30km/hr).

2. using this equation you could go at 90km/hr (30 + 90)/2 = 60 and end up with an average speed of 60, which answers the original question.

[Guest]

I don't agree with this statement for two reasons.

1. if you went an average of 75 km/hr and only traveled 120km, you would be there in less than an hour, which is imposible, because it took you two hours just to get halfway (going 30km/hr).

??? traveling at 75km/h it takes almost 2 hours to travel 120km, but the formula dictates that he travels 150 miles, which takes exactly 2 hours.

2. using this equation you could go at 90km/hr (30 + 90)/2 = 60 and end up with an average speed of 60, which answers the original question.

What's wrong with that? This is the solution that has been advocated by several people, including myself.

[Guest]

sorry I meant only 60km, not 120km (it has been edited), and on the first page the original question is 60km, I don't know where you got the 150 km from.

Average speed is defined as the distance traveled divided by the time taken.

You can't just add two speeds together and divide them by 2 to get an average, and you can't just ignore distance either.

If you have taken 1 hour to go halfway(30km/hr), and you want to be there in an hour(average 60km/hr), the only way to do that is to move from halfway to finish (30km)instantaneously, which we can ignore as a solution for this problem.

[Guest]

sorry I meant less than two hours(it has been edited), and on the first page the original question is 120km

Okay, 2 hours makes sense, but the original question is 60km, not 120.

[Guest]

For those saying the answer is 90 km/h:

You're forgetting to factor in time. You've already gone the first 30 km in one hour. So if you spent another hour driving at 90 km/h, you'd go 90 km. But you only need to go 30 km, which is 1/3 of 90 km, so you spend 1/3 of one hour driving the rest of the way.

Your total distance is now 60 km, and your total time is 1 1/3 hour, or 4/3 hour to simplify the math. 60/(4/3) = 45 km/h

[Guest]

For those saying the answer is 90 km/h:

You're forgetting to factor in time. You've already gone the first 30 km in one hour. So if you spent another hour driving at 90 km/h, you'd go 90 km. But you only need to go 30 km, which is 1/3 of 90 km, so you spend 1/3 of one hour driving the rest of the way.

Your total distance is now 60 km, and your total time is 1 1/3 hour, or 4/3 hour to simplify the math. 60/(4/3) = 45 km/h

Apparently you've not read the whole thread so I'll catch you up to speed:

Yes, we know.

We are problem solving around the question by suggesting that since there is no implicit time limit stated in the question, it is possible to bring your average speed up by driving a longer distance then is strictly necessary to reach your destination. I find the idea of a logic puzzle with the answer "it's impossible" an affront to human ingenuity.

[Guest]

90,,, would seem the correct answer. you did half at 30 and half at 90 to find average you add them together getting 120 and divide by 2 giving 60

But lets say it is 180 miles... and you drove half at 30 taking 3 hours, the other half at 90 taking one hour... 180 miles in 4 hours or an average of 45...

So, saying you take 3 hours to do the first 90 miles, how long do you have to do the second half... 180 divided by 3 hours is 60mph... and you have already used all your time... so, not possible....

So, that is the math.. but it makes no sense.... that you cant make up the time... there is none left... zero.... if you use one minute you cant get to the 60mph average..

[unreality]

there are 2 solutions:

1) It's impossible, if you are going in the straight line that's 120 km from A to B

2) If you take a detour to even it out, you can do it. The simplest way is to extend your trip so the second half is 90 km not 60 km, and then go at 90 kmh. I think that works. Well its something like that. You can do longer detours, too, if you go faster accordingly.

[Guest]

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.

It is indeed impossible. For those that need profe I worked it out.

After working it out for a bit

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.

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

choose a (speed)

now divide the 30km you need to travel by that speed

multiply this number by 60

now divide 60 by this number

write it down

multiply 30 (km/h) by this number

add your (speed)

the number you wrote down, add one and divide your last number by this number

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

** I didnt do this maths in school. I dont know how to describe what Im doing here. I just know you need take into account that you have a variable (time it takes to travel 30km) that is dependant on another variable (speed you did that 30km at) and convert the initial 30km at 30km/h into equal portions based on that last 30km. Then you can just add the total portions and divide by the whole for the final average speed.

Trying to figure this out was really hard.

[unreality]

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

[Guest]

I am so confused!!

[Guest]

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.

[unreality]

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

[rookie1ja]

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

[Guest]

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.

[Guest]

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.

[Guest]

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.

[Guest]

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.

[Guest]

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.