Discussion in 'Bad Dog Cafe' started by Junkyard Dog, Mar 13, 2019.

1. ### Lake Placid BluePoster Extraordinaire

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So...... Chunks was right. 2 and a bit.

2. ### rcole_soonerPoster ExtraordinaireSilver Supporter

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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.

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3. ### Junkyard DogTele-Afflicted

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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.

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4. ### Junkyard DogTele-Afflicted

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He was close. A bit is 0.125. So not a bad guess...only off by a third of a mile.

5. ### rcole_soonerPoster ExtraordinaireSilver Supporter

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Yep, I reread and got that. Word problems always got me in math.

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6. ### Steve 78Friend of Leo's

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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

7. ### Steve 78Friend of Leo's

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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?

8. ### 24 trackDoctor of TeleocitySilver Supporter

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ice cream has no bones?

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9. ### 24 trackDoctor of TeleocitySilver Supporter

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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

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10. ### Steve 78Friend of Leo's

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11. ### Steve 78Friend of Leo's

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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

12. ### BoubouDoctor of TeleocityGold Supporter

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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.

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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?

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14. ### Lake Placid BluePoster Extraordinaire

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White

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15. ### JupiterTelefiedSilver Supporter

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And don’t forget it takes time to turn around!

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16. ### boneyguyDoctor of Teleocity

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That's how I translate what you said.

No wonder I didn't figure it out.....there's actual mathematical thinking involved!!!

17. ### HoodieMcFoodieDoctor of TeleocityAd Free Member

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The bear is white. The house is at the north pole.

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18. ### HoodieMcFoodieDoctor of TeleocityAd Free Member

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He didn't tell anyone anything. He delivered a message on a piece of paper. Hand it over and get going.

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19. ### Lake Placid BluePoster Extraordinaire

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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.

20. ### SecretSquirrelFriend of Leo'sAd Free Member

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This is why I didn't become an astronomer.

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