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Discussion in 'Bad Dog Cafe' started by Junkyard Dog, Mar 13, 2019.
So...... Chunks was right. 2 and a bit.
I'm guessing the messenger travels twice as fast as the column, and travels 1.5 times the length of the column.
I didn't do any math, just shot from the hip.
The pace of the messenger is not given...nor is the pace of the troops. It can be solved without knowing them...see my solution a few posts back for explanation.
He was close. A bit is 0.125. So not a bad guess...only off by a third of a mile.
Yep, I reread and got that. Word problems always got me in math.
I see Junkyard Dog has already posted it, but I finally got it this morning as well (I think in a slightly different way).
So at the start the messenger is a mile in front of the end of the column and a mile behind his final position. The actual speed doesn't really matter but the ratio of the speeds of the column and messenger does. So I will say the column is walking at 1 mph and the speed of the messenger will be 1 x (ratio of speeds). If the column is walking at 1 mph the total time will be 1 hour. So the distance the messenger travels will also equal his speed (as he is also traveling at a constant speed for 1 hour).
Let's call the point where the messenger reaches the end of the column before he turns around 'x'. He travels there, then back to his original position, then 1 more mile. So his total distance is 2x + 1. This is also his speed (2x + 1 mph).
The column is traveling at 1 mph. Let's call the messenger's speed 's' for now. The distance traveled by the end of the column and the messenger will add up to 1 as there is 1 mile between them at the start. Depending on the messengers speed, where they meet can vary. The end of the column will have traveled 1/(s+1) and the messenger will have traveled s/(s+1) - these are the ratios of their speeds which add up to 1. (I messed up this part, several times, originally).
We have established speed and distance are the same so
x = s/(s +1)
x = (2x + 1)/(2x+1 +1)
x(2x+2) = 2x +1
2x^2 + 2x = 2x + 1
2x^2 - 1 = 0
x^2 - 1/2 = 0
difference of squares rule
(x + sqrt[1/2])(x - sqrt[1/2]) = 0
x = sqrt(1/2)
total distance = 2x + 1
= 2 * sqrt(1/2) + 1
= 2.4142 miles
Nice one Junkyard Dog (and Hoodie!), although I would call this an advanced high-school maths problem more than a brain teaser
Here's a brain teaser. Fred builds his house so that all of the walls are facing south. One day he is looking out his window and sees a bear. What colour is the bear?
ice cream has no bones?
actually you are all wrong with the answer , the guy stood there untill the back of the line caught up then ran back to the front so....... 1 mile
Think about it
It's a good answer except that the problem states he is moving at a constant speed. Still, you could argue that he is, but just takes his time to get going
I used to love and be good st these problems, right now it’s giving me a headache . I would need to sit down with pen and paper.
Here is a random page from my quantum mechanics book, yes I understood it all, sigh.
But how long did he spend telling the guys in the back the orders from the front? And wouldn't he be walking while he did as the troops were moving?
And don’t forget it takes time to turn around!
That's how I translate what you said.
No wonder I didn't figure it out.....there's actual mathematical thinking involved!!!
The bear is white. The house is at the north pole.
He didn't tell anyone anything. He delivered a message on a piece of paper. Hand it over and get going.
Maybe the recipient of the message couldn’t read. So the messenger had to read it to him. Maybe the OP misspelled “massage.” Some massages take a long time. Some go quick. I think we need more info.
This is why I didn't become an astronomer.