My little neighbor wants my help Options
MaMa
#1 Posted: : Saturday, November 11, 2006 5:48:23 PM
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Algebra 2 questions:

 A speedboat travels at 4 times the speed of the current. It travels 425 miles downriver in two hours more than it took to travel 150 miles upriver. What was the speed of the boat in still water? In the current?

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stealth
#2 Posted: : Saturday, November 11, 2006 7:00:23 PM
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#3 Posted: : Saturday, November 11, 2006 7:42:08 PM
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Zero mph



Cantrip
#4 Posted: : Saturday, November 11, 2006 9:37:45 PM
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Hmm.  I tried this for like five minutes, then realized you don't have any neighbors who are little.  You slug.  So, I'm going to think about it unless you find the answer on your own before I repost.

The trick to this problem is you have to account for the speed of the river.  If the river is flowing at speed X, and the boat can go 4X, then when it goes downriver it's travelling at 5X and when it is going upriver, it's going at a speed of 3X, right, 4-1=3.  Think of those moving walkways in airports.

Also, distance equals velocity times time: d=vt, where v equals 5X or 3X.  Time is either t, or t-2 or t-2 and t, depending on which one of the equations you set as the time anchor.  You solve for X using one of the equations solved for t. 

Too much to do in my head at the moment.  Try it and if you don't post here, I'll try it agian Sunday night.

You slug.

You should be more like Cantrip.



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Shizzle
#5 Posted: : Sunday, November 12, 2006 12:40:16 AM
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Well I started off with what Cantrip said, with the following in mind

5x(t)=425
3x(t-2)=150

After working through it I realized that I didn't really like t-2 since it would theoretically exclude all values of t <2. So I changed it a bit

5(x)(t+2)=415
3(x)(t)=150

This allows numbers <2 to be valid for t.

We need to get a value for one of the variables that we can put into one of the equations, since we are trying to find x here (speed) I solved for t initially.

(3xt=150)/3x  -  divide by 3x to get rid of it on the left

t=50/x  - simplifies to 50/x

Plug t into the first equation

5(x)((50/x)+2)=450

250+10x=450  -  Distribute the 5(x) into the ((50/x)+2). Simplifies to 250+10x

Solve for x, and you get 17.5 mph

in the current that would be 5x, or 5(17.5), or 87.5 mph


This can be verified by plugging the x value into both equations and seeing if it works. We know that it works in the 5x equation. When put into the 3x equation, it looks like this:

3(17.5)(50/17.5)=150
52.5(2.857....)=150
150=150

I hope its right...

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Cantrip
#6 Posted: : Sunday, November 12, 2006 1:18:41 AM
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"After working through it I realized that I didn't really like t-2 since it would theoretically exclude all values of t <2. So I changed it a bit"

Nice.  I think I'm in love.

I meant t and t-2 or t+2, and t, but the above shows that you're thinking and makes the math easier.

Math looks right.  So the speed of the boat in still water is 4X.  In the current it's 5X when going downstream and 3X going upstream, relative to the shore where x is the value Shizzle found in the above.  However, relative to the boat in the water, from the perspective of the captain, it's still 4X going up or downstream -relative to the water.  Remember the moving walkway above?  If you walk on one, you still walk at walking pace going with and against the flow of the belt looking down at the belt.  When you look to the sides, you see you're moving faster or slower than walking pace. Give all three answers.

Just wait until you start taking about General Relativity in your physics classes with speeds approaching the speed of light.  Your d=vt equation gets beefed up.  That's always fun.

You should be more like Cantrip.



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KYFHO
#7 Posted: : Sunday, November 12, 2006 1:53:06 AM
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MaMa
#8 Posted: : Sunday, November 12, 2006 3:46:13 PM
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Ok I wouldn't lie about this not being my homework.  If I wanted you guys to do my homework, I would just say it out loud.  My little neighbor really asked me this. 

This is seriously an Honors Algebra 1 Critical Thinking problem.

Thanks for the help guys.

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Dragon
#9 Posted: : Sunday, November 12, 2006 5:18:32 PM
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I thought you said Algebra 2

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MaMa
#10 Posted: : Sunday, November 12, 2006 5:43:10 PM
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I meant 1


I take Calculus damnit.

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Shizzle
#11 Posted: : Sunday, November 12, 2006 5:45:34 PM
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MaMa wrote:
I meant 1


I take Calculus damnit.


Calculus requires the use of a shitload of Algebra, so you must have just been too lazy to do this then?

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Dragon
#12 Posted: : Sunday, November 12, 2006 5:58:49 PM
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Dude I took honors algebra last year and i dont remember any of that shit. and yeah, why couldnt you do it lol.

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#13 Posted: : Sunday, November 12, 2006 7:14:00 PM
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bloodhands
#14 Posted: : Sunday, November 12, 2006 8:37:02 PM
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i remember that question from when i was in school, there are also questions like that on the SATs, annoying and take like 5 mins to think of which equation to use
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MaMa
#15 Posted: : Sunday, November 12, 2006 11:44:39 PM
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I did try it out, but I wasn't sure of my answers.  I didn't want to give my neighbor the wrong answers.  And yes, I did make a mistake.

Fear the ING!
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