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The entire span of time is represented by 1 + z, with 1 hr being upstream (for the rower) and z hr being downstream.
For this span of time, the stick travels 1 mile, and thus you represent the equation as:
y mi/hr * (z + 1) hr = 1 mi -
Solving the earlier equation down...
z hr * (x + y) mi/hr = (x - y + 1) mi
zx + zy = x - y + 1
y + zy = x - zx + 1
y (1 + z) = x - zx + 1Substituting in the later equation where y(z+1)=1...
1 = x - zx + 1
0 = x - zx
x = zx
z = 1 -
With z=1, plug it into y(z+1)=1 to get...
y (1 + 1) = 1
y * 2 = 1
y = 1/2 mi/hr -
I believe there's your answer, unless someone points out that I missed something...
It's been about 20 years since I was in Algebra class... Thanks for the mental rejuvenation! 👊👍
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Looking back, it looks like Vince Carolli and Xambler landed on the right answer as well... Vince seems to have accidentally landed on the assumption about the rower's speed that incidentally didn't matter (as Xambler pointed out), but not sure if Xambler's answer would satisfy our fine teachers in terms of "showing our work" 😝
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aTOM's solution in English:
CS =Current Speed
RS=Rowers SpeedThe rower and stick meet at point A
- In 1 hour the rower is RS-CS distance from A
- The stick is CS from A
-- therefore their distance apart is RS-CS+CS or simply RSTo meet again the rower speed is RS+CS
- the stick is CS
-- therefore they will meet at the start at RS+CS+CS
--- or simply RS+2CSSo...
We have determined the stick travels 1 CS while the rower is rowing out plus 1 CS while rowing back and the story says that it started 1 mile out.
- therefore 1 =2CS
-- Simplified to 0.5 =CSWe can conclude:
The current speed (and the speed of the stick) is 1/2 mph
The rower speed in 1 mile is RS-CS or 1= RS-0.5 or 1.5=RS or 1-1/2 mph
The distance the rower travels out from the stick is RS-CS or 1.5- 0.5 or 1 mile
The total distance rowed out and back is 1+(RS-CS)+(RS+CS) or 4 miles -
Doc Xray wrote:
Assuming the rower travels at a constant rate of speed (both upstream and downstream, which is bogus), then the stick is traveling at 1/3 the speed of the rower (moves one "segment" while the rower moves 3 segments). We're told that the rower is traveling at 1 mile per hour, thus the current (stick) is moving at 1/3 mph. Reality would require the rower to travel downstream faster than upstream. If you assume constant effort by the rower (without tiring), and also assume the rower moves twice as fast downstream as upstream, then the stick moves one segment in the same amount of time as the rower moving two segments (1 at speed x, and 2 at speed 2x). Therefore, the current is moving at 0.5 mph. Too many assumptions to resolve exactly!
With all due respect, I think this is the right answer with some flawed assumptions...
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It wasn't stated that the rower was traveling at 1 mile per hr, but rather that he/she traveled for a duration of 1 hr before turning around toward the starting point. Therefore it cannot be assumed that the rower traveled exactly 3 equal size segments compared to the stick traveling 1 segment.
In the end it works out that way, but it could have been different if some of the constants were defined differently.
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Sorry but Ꭵ got .33 too!
1 mile up stream (met the stick), carried on for another hour (so prseume thst mile took 1 hr), then back (1+2=3 hours). The stick took 3 hrs to travel 1 mile (1*3= .3333)
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aTOM boomb wrote:
This is very impressive sir. However, checking your work, I found a flaw. You can't divide both sides by a variable in case that variable is 0, in which case the answer would be undefinedSolving the earlier equation down...
z hr * (x + y) mi/hr = (x - y + 1) mi
zx + zy = x - y + 1
y + zy = x - zx + 1
y (1 + z) = x - zx + 1Substituting in the later equation where y(z+1)=1...
1 = x - zx + 1
0 = x - zx
❗x = zx❗
z = 1 -
I think all of you are missing something. I was missing it too until TTK brought it to my attention. The rower sees the stick after she's already rowed for a mile. Therefore, the stick travels the current speed while the rower goes for 2 hours and 1 mile
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ωⅇɢṡɪⅇṣ wrote:
What?!? If this is true, you may have just found a loophole in the space/time continuum! Reality as we know it is wrong. This would change everything about everything!!!I think all of you are missing something. I was missing it too until TTK brought it to my attention. The rower sees the stick after she's already rowed for a mile. Therefore, the stick travels the current speed while the rower goes for 2 hours and 1 mile
Can we trust the circles anymore? Are they really ovals? Does Nick exist? Opens up so many questions here...
❔✨❔🌀❔⚡❔🌀❔✨❔💤 -
ωⅇɢṡɪⅇṣ wrote:
I think all of you are missing something. I was missing it too until TTK brought it to my attention. The rower sees the stick after she's already rowed for a mile. Therefore, the stick travels the current speed while the rower goes for 2 hours and 1 mile
I stand by my answer and I think I laid out enough work. And I don't see a problem with dividing both sides by a variable.
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Has anybody found the answer
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I have, just can't find wegsies on pal
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Wow just wow this all made my head spin. Flashbacks of high school algebra.
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Turns out I won't be getting the correct answer until next week. I'll let you all know if anyone got it right, and if so who. I'll show how to solve it if anyone is interested too👍
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Damn! I dont like no.'s 😖
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I say it's 0.5 so yeah I funna be right and you watch!
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ωⅇɢṡɪⅇṣ wrote:
Hint #2 - all calculations progress from the time the rower first sees the stick. It is irrelevant what happened before that point in time (from a math perspective). Sorry...my parents were both teachers so any help I ever got from them came in small hints and nudges :)I think all of you are missing something. I was missing it too until TTK brought it to my attention. The rower sees the stick after she's already rowed for a mile. Therefore, the stick travels the current speed while the rower goes for 2 hours and 1 mile
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I trust aTOM. He's Asian. And we all know that Asians are the smartest people on the planet.
Except this One Asian guy that I tried to cheat off if in my college algebra class on the final in 1997. I copied him and I got a C. Hopefully that wasn't you aTOM.
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Dirty Balls wrote:
A dumb asian? Probably the same one that disgraced his family by moving to America and becoming fatI trust aTOM. He's Asian. And we all know that Asians are the smartest people on the planet.
Except this One Asian guy that I tried to cheat off if in my college algebra class on the final in 1997. I copied him and I got a C. Hopefully that wasn't you aTOM.
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Dirty Balls wrote:
I trust aTOM. He's Asian. And we all know that Asians are the smartest people on the planet.
Except this One Asian guy that I tried to cheat off if in my college algebra class on the final in 1997. I copied him and I got a C. Hopefully that wasn't you aTOM.
You went wrong as soon as you said "took algebra in college"... The "smarties" take algebra in kindergarten
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Lmao
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0.414
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aTOM boomb wrote:
That's what I said without the equation 👍With z=1, plug it into y(z+1)=1 to get...
y (1 + 1) = 1
y * 2 = 1
y = 1/2 mi/hr -
ωⅇɢṡɪⅇṣ wrote:
If it was zero then it would be dividing zero by zero which would be zero not undefined I think he's got it👍aTOM boomb wrote:
This is very impressive sir. However, checking your work, I found a flaw. You can't divide both sides by a variable in case that variable is 0, in which case the answer would be undefinedSolving the earlier equation down...
z hr * (x + y) mi/hr = (x - y + 1) mi
zx + zy = x - y + 1
y + zy = x - zx + 1
y (1 + z) = x - zx + 1Substituting in the later equation where y(z+1)=1...
1 = x - zx + 1
0 = x - zx
❗x = zx❗
z = 1 -
How Many miles did she go?
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👻🎅💰⚾⛳🏄〽🐸🐯🐺🐮🐵👨👶👵 wrote:
How Many miles did she go?
Doesn't matter how many miles, the solution remains the same.
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wegsies did you get the answer to this yet?
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