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Speeding up

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Speeding up - Back to the Cool Math Games

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?

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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 ;)

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)

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And what will my average speed be if I go 90 km/hour for the second half of the trip? Wouldn't it be 60km/hour?

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The two cities are separated by 60 km. If I have traveled half way (30 km) at 30 km/hr then I have spent 1 hour traveling. To reach an average speed of 60 km/hr in the total travel (which is 60 km) I need to spent one hour in total. But I already spent 1 hour in half of the travel. Unless I move instantaneously (infinite velocity) from the half of the travel to the other city, there is no solution.

Traveling at 90 km/hr (the second half) gives an average of 45 km/hr.

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If you go 90 km/hr for the second half of the trip your average speed would not be 60 km/hr. Here's why:

Average speed = total distance / total time

Your total distance would be 60 km. The first half of the trip takes 1 hr of course, but the second half takes less time since you are traveling faster, it takes only 1/3 hr. And 60km/ (1+1/3 )hr = 45 km/hr.

Another way to explain why it is impossible, is to use algebra:

Let r = rate of second half. So the time for the second half is 30/r.

Again, using the formula:

average speed = total distance / total time

60 = 60 / (1 + 30/r)

60(1+ 30/r) = 60

1 + 30/r = 1

30/r = 0

Which is impossible. (The rate of the second half cannot be 0)

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to get the mean/average you need to add them and divide by 2 to get 60. to do this do it in reverse so you double 60 to get 120 and you know one is 30 so you have 90 left and thats the answer!!!!!

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If you go 90 km/hr for the second half of the trip your average speed would not be 60 km/hr. Here's why:

Average speed = total distance / total time

Your total distance would be 60 km. The first half of the trip takes 1 hr of course, but the second half takes less time since you are traveling faster, it takes only 1/3 hr. And 60km/ (1+1/3 )hr = 45 km/hr.

Another way to explain why it is impossible, is to use algebra:

Let r = rate of second half. So the time for the second half is 30/r.

Again, using the formula:

average speed = total distance / total time

60 = 60 / (1 + 30/r)

60(1+ 30/r) = 60

1 + 30/r = 1

30/r = 0

Which is impossible. (The rate of the second half cannot be 0)

Forgive my ignorance, but I'm still a little confussed.. <--- NOT A MATH TEACHER If you have the ability to speed up the average by doing 90 to make it 45, can you not speed it up more thus raising the average. When it comes to Algebra, I have the mental aptitude of a Lego Block.

Ahhhh, WAIT.....................I GET IT!!! All the Letters and Numbers are a fancy way of saying YOU JUST DO NOT HAVE ENOUGH TIME TO RAISE THE AVERAGE THAT HIGH BECAUSE THE FASTER YOU GO THE LESS TIME YOU HAVE TO ACHEIVE THE DESIRED AVERAGE....

And I was starting to think all that porn I watched instead of doing my homework was a Mistake! Sheeeeeesh. IMAGINE THAT!

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to get the mean/average you need to add them and divide by 2 to get 60. to do this do it in reverse so you double 60 to get 120 and you know one is 30 so you have 90 left and thats the answer!!!!!

I'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.

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yes impossible

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Not possible, here's a simpler explanation:

To get speed, divide distance by time => d/t = 60 km/hr

The distance is easy => 60 km

The time to have a speed of 60 km/hr then is also easy => 1 hr

The problem then becomes evident. By going at 30 km/hr for half of the total distance (30 km), you have already used up 1 hour of time, so no matter how fast you go, your total average speed will be less than 60 km/hr. Unless like rookie1ja mentioned, you mess with relativity and get to your destination without having any time elapse =P (i.e. going back in time and then reaching your destination)

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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.

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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.

ur not reading it wrong ur just not getting it

the town is 60 km away and for 1 hour you travel 30 kph so ur halfway. the only way to get sixty would be to travel for another hour at 90 kph but if u did that you would 60 miles past the town and if u slow don then the average speed would be less then 60 so it is impossible

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ur not reading it wrong ur just not getting it

the town is 60 km away and for 1 hour you travel 30 kph so ur halfway. the only way to get sixty would be to travel for another hour at 90 kph but if u did that you would 60 miles past the town and if u slow don then the average speed would be less then 60 so it is impossible

Now hold on a sec! Who said you had to go straight there?? There is only one road in your town?

Besides which, what if you want to measure the mode average instead of the mean Then it doesn't matter how long you drive or at what speed as long as you spend more time at 60hm/hr then at any other one given speed.

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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.

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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

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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.

I'm sorry, you'll have to read the question again. It doesn't ask how you can get there in an hour, it asks how you can get there traveling at an average of 60km/hr. And the answer is you make your trip longer. It's only impossible for those with small imaginations.

Now, perhaps it was meant as a trick question, in which case the question will have to be reworded to put a time limit, or to exclude the possibility of extending your trip.

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to sum it up here are the possibilities:

1) Instantaneously warp from current point (time = 1h, distance traveled = 30km) to destination

2) Continue to your destination but reverse time to the point where your averages becomes 60 km/h

3) Detour to lengthen travel time to average out to 60 km/h

number 3 being most reasonable

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to sum it up here are the possibilities:

1) Instantaneously warp from current point (time = 1h, distance traveled = 30km) to destination

2) Continue to your destination but reverse time to the point where your averages becomes 60 km/h

3) Detour to lengthen travel time to average out to 60 km/h

number 3 being most reasonable

Precisely! Humbug to impossible!

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to sum it up here are the possibilities:

1) Instantaneously warp from current point (time = 1h, distance traveled = 30km) to destination

2) Continue to your destination but reverse time to the point where your averages becomes 60 km/h

3) Detour to lengthen travel time to average out to 60 km/h

number 3 being most reasonable

THATS FUNNY. REDICULOUS AT BEST. "WARP" lol,,, "While your at it, just hook up a Flux-Capacitor" to your forehead and run 88 MPH Backwards, and maybe you can GO BACK IN TIME and just travel 60 the entire trip" Clowns....

"Humbug to Reality Void Answers"

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Form the original question:

how fast do I have to go for the rest of the way

aesculapius' answer:

to sum it up here are the possibilities:

1) Instantaneously warp from current point (time = 1h, distance traveled = 30km) to destination

2) Continue to your destination but reverse time to the point where your averages becomes 60 km/h

3) Detour to lengthen travel time to average out to 60 km/h

number 3 being most reasonable

Sorry you didn't answer the question "How fast?" in any of your possibilities. You are adding too many variables and hypotheticals, so just accept the original solution. This problem was supposed to get you to make wrong assumptions in averaging speeds and it obviously worked on some people.

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the answer i proposed was just an extension of the original solution involving time and space relativity. "warping" isn't good terminology to use but what i mean't was just break from current location to final instantaneously and warp kind of implies that, but isn't exactly a good word to use. i never said the no solution was incorrect under current real-life circumstances

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I will drive with speed 1800Km/Hours or above.

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So why can't you just drive at 90km/hour for one hour and at the end of that hour you end up at your destination? Reading the question I don't see any rules against doing this.

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can't be done you've already used your hour

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can't be done you've already used your hour

These is no time limit posted in the question! Who's hour did you use?!?! Oh no, it's not like there is another hour coming right after this one or anything! Jeez, when you guys get a notion into your head...

Is the object of these puzzles to get you to give up, or to think in perpendicular directions?

I submit that an answer which is reasonable and violates no premises of the question is a proper resolution to the question. If you do not agree, please tell me specifically which conditions will cause the question to be regarded as solved.

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THATS FUNNY. REDICULOUS AT BEST. "WARP" lol,,, "While your at it, just hook up a Flux-Capacitor" to your forehead and run 88 MPH Backwards, and maybe you can GO BACK IN TIME and just travel 60 the entire trip" Clowns....

"Humbug to Reality Void Answers"

Apparently you have trouble recognizing sarcasm, maybe you should consult an optometrist...

But just to clue you in, the point of the post was to support a detour solution, and the other two suggestions were for humorous effect.

Just FYI, a flux capacitor would be no good at all, it would take you back to the FUTURE, not the past... <--- That's a joke

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