How Much Farther?
Two friends were 59 miles apart before Karl started. Karl travels 7 miles every 2 hours. Ragknot travels 8 miles every 3 hours. Ragknot started an hour later than Karl.
How many MORE miles will Karl travel before he and Ragknot meet?
(amendment: --> they are traveling in a straight line towards each other)
How many MORE miles will Karl travel before he and Ragknot meet?
(amendment: --> they are traveling in a straight line towards each other)
posted by Zaux at
3:38 PM
32 Comments:
I guess this means MORE miles after Ragknot has started. By then the two friends (?) are 52 miles apart.
Their combined speed is 7 + 8/3 mph so the time till they meet is 52 / (7 + 8/3) hours = 156/29 hours.
So the distance for Karl will be 7*156/29 = 37.655 miles.
this is what i got somehow?
altogether,Karl will travel 22.5862 miles MORE than Ragknot
What if they're going in arbitrary directions, or the same direction (like the dog and rabbit)? If so, which one was ahead? They may never meet again (OK the queston implies that they will meet).
Remember this is ToM. But I'm too lazy, I mean busy, to do the math.
sorry ..post error .. I will correct
sorry guys ... the problem statement is now correct
Hi Wiz ... sorry you had done the work with the wrong info ... guess I was in too big a hurray.
Looks like I am an hour late.
I think we will meet in 6.37 hours.
During that time Karl will have traveled 44.66 miles and I will have traveled 14.34 miles.
So Karl will have traveled 30.31 miles more.
(30.31034)
I assume we are walking toward one another, and we don't halt for a break.
Zaux. Are they travelling towards each other, or is one chasing the other?
Chris,
Karl is traveling more than 2.6 times faster than me... and started an hour before me. If we aren't moving toward each other, we will never meet. Of course Karl may not be coming directly toward me, but at some angle, then we could meet. But if so, we would need more info to solve the problem.
... aren't I the stubborn one. I'm sure you're right though Ragknot.
Of course you'd meet. Karl is faster, so if he was chasing you, he'd eventually catch up.
I say 7.22 Miles?
Just a guess
Zieu
Mr. Nit Picker says: MORE: does that mean the extra miles he walked after Ragknot started, or how many more miles than Ragknot walked?
LOL. I'm only doing this for a wind-up.
Chris,
If Karl was coming toward me, and I was going the other way, you are right, he would catch me.
But I figure Karl will travel for 6.379310345 hours and cover 44.65517241 miles. I will travel 5.379310345 hours and cover 14.34482759 miles.
For a total of 59 miles.
Karl will have covered 30.31034 miles more than I.
Mr. Nit Picker also reminds you that they may be walking along two different sides of a triangle, but on a collision course. I'll neglect the Earth's curvature, for now.
OK. If Karl is chasing Ragknot, then he will have reduced the 59 miles to 55.5 by the time Ragknot starts. The speed difference s i3.5 - 2.666... = 0.833333.. mph, so that'll take 55.5/0.8333 == 66.6 hours to catch Ragknot. We're just down to what MORE means.
Altogether Karl walked 3.5 + 66.6*3.5 = 236.6 miles, and Ragknot travelled 66.6 * 2.666... = 177.6 miles.
So if MORE means altogether, then Karl walked 236.6 - 177.6 = 59 miles or it could mean 55.5 since Ragknot set off.
I haven't looked at any other result. But assume someone did it right for them walking towards each other.
Ooops, MORE could also mean 236.6 - 3.5 = 233.1
Did I tell you the one about the polygamist I met on my way to St. Ives?
I see I missed something. It says now says Karl moves 7 miles every two hours.
It said "Karl travels 7 miles every hours." when I copied it. so I used 7 mph. I suppose the post was changed.
Changing Karl's speed makes it 10 hours to meet. Karl travels 35 miles and I travel 24 miles. Karl travels 11 miles more than me.
I don't read most post. (I don't want to see someone else's answer),
but now I quickly reviewed other post and see that it was corrected.
I am sorry to post "30+ miles more", even after I should have read the correction. I now say 11 miles.... after my own correction. But now I am laughing at myself. Good job Zaux, you tricked my mind.
If they were heading directly towards one another, then combined speed is 3.5 + 2.666... = 6.1666..
and so they'd take 55.5/6.1666... = 9 hours to meet.
So Ragnot will have travelled 8/3*9 = 24 miles, Karl 3.5 + 3.5*9 = 5.5 + 31.5 = 35 miles.
The rest hinges on what MORE means.
5.5 was a typo, should have been 3.5.
I see Ragknot has spotted the changes in the question.
Chris and I have the same data,
Karl 35 miles and 24 for me.
I said 10 hours from the time Karl began. Chris said 9 hours (must be from the time I began.
Don't have a published answer for this one ... I got 31.5 miles more.
Karl's rate of travel = 3.5 mph.
He travels 1 hr. before Ragknot begins.
So when Ragknot begins, Karl has already moved 3.5 miles closer ... the dividing distance is now 55.5 miles.
55.5 = 7/2 + 8/3 * T (time)
T= 9 ... thus in 9 hours they meet.
9hr.*3.5mph = 31.5 miles
Thus Karl will travel 31.5 more miles before they meet.
Aaaah. That's what MORE means.
sorry Chris... thought that was clear
wow... this problem statement was surely flawed ... I should have stated they were moving in a straight line towards each other.
If we had known that the statement had been made at the time Ragknot started, we might have concluded that Karl had already traveled for one hour, and the question was "How many MORE miles will he travel....
But because it states "Ragknot started".... past tense. If it had said "Ragknot now starts and Karl has been traveling for an hour...
Yes, it was flawed, but still fun to try.
Wiz had the right idea when he said...
"I guess this means MORE miles after Ragknot has started. By then the two friends (?) are 52 miles apart."
But he said that when Karl was moving 7 MPH. He had the right answer to the wrong question.
LOL
I was enjoying the fact that the problem statement was horribly flawed :)
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