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Fun math problem that stumps everyone
Old 04-25-2022, 03:39 PM   #1
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Fun math problem that stumps everyone

I stumbled upon this simple looking math problem last week and showed it to several people and have not found anyone that got it right, including my daughters 6th grade math teacher. It took Albert Einstein an hour to figure it out.

If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?
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Old 04-25-2022, 03:41 PM   #2
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It's not possible.
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Old 04-25-2022, 04:04 PM   #3
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Funny, it looks like it's relatively simple, with the wrong but simple answer to be 90 as 90 + 30 averaged is 60.
But that is the Wrong answer.

I think if Einstein was working on the faster than light makes time go backward, I can see why he spent an hour on it.

For me, there is no answer.
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Old 04-25-2022, 04:10 PM   #4
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^^^^^Agreed it seems easy that 90mph is the answer but I'll need to think on it,,,,, I guess.
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Old 04-25-2022, 04:17 PM   #5
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As Braumeister says, it can't be done. Averaging 60 mile/hour = 1 mile/minute, so it requires 2 minutes to go two miles. However, 30 mile/hour = 0.5 mile/minute, so covering the first mile already took you 2 minutes. It would require infinite speed to achieve zero time over the second mile, but nothing travels faster than light at ~670 million miles/hour. Ergo, it cannot be done.

It took me longer to type this than it did to figure it out.
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Old 04-25-2022, 04:19 PM   #6
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Quote:
Originally Posted by braumeister View Post
It's not possible.
+1. In the first mile you've already used up your 2 minutes needed to avg 60 mph in 2 miles. I had the answer before seeing this post, so I guess it didn't stump everyone.
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Old 04-25-2022, 04:23 PM   #7
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My favorite (and I wish I had a copy of it) was a simple series of additions and subtractions on a strip of paper. As each operation was completed, the paper was rolled to the next operation that used the result from the previous operation. Seriously, there were no tricks within the operations. I never saw anyone in my Jr. Hi class get it right - including two math teachers.

It turned out to be one of those crazy things where your mind leaps ahead (perhaps making you end up with 4000 instead of 3100 or perhaps 3900. I forget just how it worked but I never saw it fail. - even when everyone had heard about it.) YMMV
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Old 04-25-2022, 04:26 PM   #8
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Originally Posted by Gumby View Post
As Braumeister says, it can't be done. Averaging 60 mile/hour = 1 mile/minute, so it requires 2 minutes to go two miles. However, 30 mile/hour = 0.5 mile/minute, so covering the first mile already took you 2 minutes. It would require infinite speed to achieve zero time over the second mile, but nothing travels faster than light at ~670 million miles/hour. Ergo, it cannot be done.

It took me longer to type this than it did to figure it out.
Conceptually, this was my thought process too. Should have posted it sooner.
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Old 04-25-2022, 04:29 PM   #9
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If you drive 2 miles at 60 mph it takes 2 minutes to cover that distance.

You've already driven 1 mile at 30 mph. That took 2 minutes.

Problem can't be solved.
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Old 04-25-2022, 04:58 PM   #10
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Completely missed the 2 minute component but I get it takes 2 minutes to go the first mile at 30mph. Word game...
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Old 04-25-2022, 05:00 PM   #11
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Looks like we are good with numbers on this forum, not surprising I guess since early retirement has a lot to do with math.
I worded it wrong in the title when I said stumps everyone, should have said almost everyone.

If you ask your family and friends, chances are they will say 90.
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Old 04-25-2022, 05:15 PM   #12
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This turned out better than I thought. I get really irritated with FB type feeds where they’ll show you a math problem but never the answer. So they get numerous answers but no one is sure which one is the right answer or why. Even though I like those type of problems, I skip them because there is no answer given.
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Old 04-25-2022, 05:16 PM   #13
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I did the time thing and found it impossible too.

But hey, I'm an engineer and that's what they pay me for -

Although an engineer would say "light speed". But the math guy would say, even light speed would add time.

And the engineer would reply the the difference was insignificant -
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Old 04-25-2022, 06:58 PM   #14
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No way it took Einstein an hour to figure it out unless his first name was Joe.
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Old 04-25-2022, 07:15 PM   #15
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And if you think it took Einstein an hour to solve, I have a just-over-one-mile-long bridge in Brooklyn that I can let go for cheap.

EDIT: cross-posted with Zinger.
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Old 04-25-2022, 07:33 PM   #16
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He could have been trying to apply special relativity and determining if time dilation effects could cause the observed clock inside the 30mph vehicle to be slightly under 2min, thus allowing a theoretical less than light speed second mile to get in at 2min for 2 miles.
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Old 04-25-2022, 07:39 PM   #17
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Quote:
If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?
So I'll post before looking at the responses.

This isn't that hard, I doubt it took Einstein an hour (proof of that?).

60 mph is a mile a minute. So to average 60 mph over 2 miles will take 2 minutes.

You traveled the first mile at 30 mph. Well, if 60 mph is a mile a minute, 30 mph is a mile in two minutes. You already used up all the time, you can't average 60 mph with only one mile to go (or one foot to go!). Can't be done, at any speed.

A similar problem is using mpg. Get 20 mpg on to a destination that is a run up a hill or against a head-wind, and 40 mpg on the way back does *not* give an average of 30 mpg. A "mpg" figure doesn't work that way, since the distances don't match the distance traveled on a gallon. You'd have to go 20 miles @ 20 mpg, and 40 miles @ 40 mpg to average 30 mpg. The distances are different.

It's also why going from a car with 20 mpg to one with 40 mpg is not the same fuel savings as going from 10 mpg to 20 mpg.

This leads people to make bad decisions.

Now, I hope I got all that right, or I'll be embarrassed! At least I avoided using affect and effect!

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Old 04-25-2022, 08:00 PM   #18
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I was going to suggest it's just folklore that Einstein was presented with this problem, but maybe not. https://fs.blog/einstein-wertheimer-car-problem/ documents a similar problem. I doubt it took Einstein an hour, but if this story is true, did take him more than a moment. Perhaps being sent the question by a colleague made him think there must be an answer.
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Old 04-25-2022, 08:25 PM   #19
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Old 04-25-2022, 08:33 PM   #20
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I was going to suggest it's just folklore that Einstein was presented with this problem, but maybe not. https://fs.blog/einstein-wertheimer-car-problem/ documents a similar problem. I doubt it took Einstein an hour, but if this story is true, did take him more than a moment. Perhaps being sent the question by a colleague made him think there must be an answer.
I didn't get any sense it took him anywhere near an hour. The article states that he replied, “Not until calculating did I notice that there is no time left for the way down!”

You could say it wasn't immediately obvious to him that the solution would not be some reasonable speed. But "not until calculating it", could have been just a few seconds.

I'll also take exception to those using the phrasing that "there is no answer", or that it "can't be solved" (versus "it can't be done" - with "it" being "go fast enough to average 60 mph").

There is an answer to the problem, and the problem can be solved, and that answer is that there is no way to average 60 mph at that point. Engineers do calculations all the time which show that a thing cannot be done. That's the solution. It keeps people from wasting time and resources trying to do something which cannot be done (no, not even if you just "try hard enough").

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