Catching Up
A runner was told that the last running record was made with an average of 30 miles per hour. He ran 15 miles per hour for the first half of the race, how fast he must run in order to break the last record ?
Labels: logic, mathemagic
posted by Rajesh Lal at
12:15 PM
14 Comments:
He must go 45.00001 miles per hour for the last half of the race.
If he goes only 45 mph then he sould tie the record.
It's impossible - the previous record would have exactly finished by this point.
He would have to go at infinite mph!
Yanon Mous
the first record is impossible. no human can run that fast
it is impossible to break the record at this point
If we say that the first race was 30 miles then the first guy did it in an hour. If half way up the race the second guy was running 15 mph then he already got through one hour. It is impossible to break the record then.
This question seems a bit ambiguous. It seems that all but Patrick are under the impression that "half the race" means "half the distance of the race". If that is indeed the correct interpretation, then the runner cannot physically make up the time. However, it is my belief that "half the race" means "half the time". If this truely is the question, which I firmly believe, then I agree with Patrick to an extent.
If we ignore time lost due to acceleration, then the runner must run at an average speed of more than 45 mph for the remainder of the race. But how much faster? From a theoretical stand-point, there is no actual definition as we can always come up with a smaller increment. However, if we are looking at it from a practical scenario (which we are), in order to find the exact speed we would need to know the accuracy of the sensors involved as well as the scale of the race (100 yards or 3,000 miles) as it will have an impact.
Anywho, my answer is this: the runner must run at an average speed faster than 45 mph.
I interpret "half the race" as half the distance. My first thought was that he has to go faster than 45 mph, in order to break the 30 mph average.
However, in terms of a race, i agree with anonymous: the previous runner would have already finished (if he was going twice as fast, it would take half the time, which is where the other guy is at).
So it really depends on if you are looking at it only in terms of overall average speed, or actually wining the race.
too bad for him because by the time he reached the half way lane marker, the other dude won the race duhh. and to think im in middle school lol
Yeah, middle-schooler...it takes your infinite genius to read what everyone else has said and repeat it. I am in awe of your magnificent brain-power.
WHY OH WHY do people insist on repeating correct answers that are already posted, as if they are the ones who thought of it first? Some adolescent desire to prove they are somehow better than everyone else?? Oh yeah, you ARE adolescents. I forgot, lol. Maybe you should start your own little-kid puzzle site, and then you all can claim you're smarter than each other and stop annoying us with your sorely misplaced arrogance.
If someone talked about the 100 meters in 10 seconds, you would probably say half the race was 50 meters, rather than 5 seconds.
Yanon Mous
p.s Adolesence rules!
I think anything more than 15 mph because 15+15=30 mph sooooo.....
A general question (or two):
Why do people assume that these two runners are in the same race?
Also, why do people think the distance run makes any difference?
Whether the race is 100 meters or 100 kilometers makes no difference to setting a record.
P.S. - The point of the blog is to make people think. For someone to post the answer after someone else did means that they figured it out, and then posted it.
Just because (this time) I was first to post the answer, does that make me right or does that make me wrong?
I will post the answer that I come up with (either correct or not; stay tuned!) for one extremely simple reason...
THAT IS THE POINT OF THIS BLOG!
Well if one person is going at X mph, and someone else is going at 1/2 of X mph, for the slacker to catch up, he would have to go at twice the speed that the winner is going at.
because this seems impossible for a human to accomplish, lets replace it with cars instead of runners, to stop people moaning about how its impossible.
X=30
so 1/2 of X=15
2X=30*2=60.
so the slacker, to catch up with the winner, hasto go at 60mp/h
it doesnt say that the record holder ran 30mph all the way through the race though does it, it says an AVERAGE, so all you idiots that think the question is stupid are in fact stupid themselves for not reading the question correctly. for all we know the runner could of jogged the first half at a very slow pace then ran alot faster for the second half of the race.
I dont think its wrong for people to post their own answers, or choose to agree/disagree with answers already posted...but it IS ridiculous when 10 people have just agreed on the same answer for someone to repeat that answer as if YOU were the only one right, and belittle everyone else as if they were wrong, with childish comments like "duhhh". And that is of course followed by the seemingly obligatory (on this site) bragging of one's own inexperience and immaturity. Frankly I think that most of the people who say that are probably much older, and are trying to somehow impress people. It seems like actual kids wouldnt be so enthusiastic about sharing their age. At least the smart ones wouldnt be.
As far as this problem goes--I cant believe people still dont understand. It doesnt matter 1)how long the race is 2)if there are other people running at the same time, 3) that it is the average speed, or 4) if its humanly possible. Its obvious that it SEEMS like hed have to run over 45 mph to break the record, and this reasoning would stand if he had ran even a little faster than half of the record holder's overall (average) speed. However, because the speed of the runner is only half that of the record holder, then in the time that the record is held for the runner has only completed half the race. Yes the record holder may have gone slower and faster in some parts, but because the average speed is what it is, he must complete the race by that time. And that time will have only allowed our 15mph runner to complete half. In other words it is impossible for him to break the record because as he crosses the halfway mark that record-time is passing. Unless he can transport himself instantaneously. If he had reached this point just a moment earlier, there would have been some speed that he could have beat the record with.
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