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Author Topic: Help me solve this math problem
geekwannabebritt
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Icon 5 posted August 27, 2004 18:42      Profile for geekwannabebritt         Edit/Delete Post   Reply With Quote 
I need help on my summer math homework. Can someone please help explain how to work out this problem:

Sam leaves home and drives at a constant speed to his grandparents' house. On the way, he stops at a mall to buy a gift for his grandparents. Four hours after stopping at the mall, Sam has traveled 300 miles from home, and 7 hours after stopping at the mall, he has traveled 465 miles from home. How far is the mall from Sam's house?

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*/\~Brittney~/\*

Posts: 95 | From: Washington | Registered: Jul 2002  |  IP: Logged
dragonman97

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Icon 1 posted August 27, 2004 18:46      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Technically, it is impossible for him to travel at constant speed [Big Grin] . Unless, of course, the clock starts after he passes the 'zero' point which is at the end of a runway/acceleration area, and a similar configuration is present at his destination, where once he passes this point, he slows down. Maybe I'll look over the real problem while I have dinner [Wink] .

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There are three things you can be sure of in life: Death, taxes, and reading about fake illnesses online...

Posts: 9329 | From: Westchester County, New York | Registered: May 2001  |  IP: Logged
drunkennewfiemidget
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Icon 1 posted August 27, 2004 20:08      Profile for drunkennewfiemidget     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by geekwannabebritt:
I need help on my summer math homework. Can someone please help explain how to work out this problem:

Sam leaves home and drives at a constant speed to his grandparents' house. On the way, he stops at a mall to buy a gift for his grandparents. Four hours after stopping at the mall, Sam has traveled 300 miles from home, and 7 hours after stopping at the mall, he has traveled 465 miles from home. How far is the mall from Sam's house?

If you're having a hard time with this question, you're probably thinking about it too much.

Most of the answer is in the last bit.

If he has gone 300mi 4 hours after the mall and 465 7 hours after the mall, he's gone 165mi in 3 hours. That means he's going 55mph.

So, 4 hours from the mall = 4 hours * 55mi == 220mi.

If he's gone 220mi in 4 hours, and he's 300mi from home, then the mall is 80mi from his house.

Posts: 4897 | From: Cambridge, ON, Canada | Registered: Jun 2004  |  IP: Logged
Ivan
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Icon 1 posted August 27, 2004 20:18      Profile for Ivan   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
I got 80 miles.

First I found the difference b/t the miles at 7 hrs and 4 hrs. Then I found the m.p.h. of that. Multiplied by 4 hours and subtracted from 300.

But, then again, I got a 78 on one of my Pre-Cal tests earlier >_>; Not entirely my fault though. The teacher graded it weird. It helped everyone elses grade, but actually lowered mine [Roll Eyes]

EDIT: Oops sorry DNF. Had my answer all typed up and forgot to Submit Post. So, there you have it. Straight from two sources, so it must be true.

Posts: 269 | From: North Carolina | Registered: Mar 2004  |  IP: Logged
geekwannabebritt
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Icon 1 posted August 27, 2004 20:18      Profile for geekwannabebritt         Edit/Delete Post   Reply With Quote 
wow, im stupid!
well thanks for the help! I understand it much better!

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*/\~Brittney~/\*

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dragonman97

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Icon 1 posted August 27, 2004 21:18      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
And I got the answer a good while ago, it's still sitting on the table, scrawled on the back on a junk mail envelope [Wink] . However, my post was *not* going to be the answer, but to recommend a thought process instead. *shrug* When you have a problem like this, you need to recognize what information you've been given, and exactly what they're asking for. It can often be helpful to sketch out a problem like this. In this case, I drew 3 points (Sam's home, the mall, and his grandmother's house), and drew a line from his house, past the mall, to 2 points between the mall and the final destination. Marking the first span 300 mi, and the same span up to the second point 465, it becomes immediately apparent that there is 165 miles in between. Next, I connected a line from the mall to the first point, marking it as 4 hours, and then continued the line to the second point, marking it as 7 hours. This makes the 3 hour difference pretty clear. Now, you can see that 165 mi is crossed in 3 hours, and some quick math tells you 55 mph. Then, based on the knowledge that he's going 55 mph, and that it took him 4 hours to go from the mall to point 1, we know that he went 220 miles between these location. Since we know point 1 to be 300 miles from his home, we know that his home is 80 miles from the mall.

Bah...it would have been faster for me to have done this...wouldn't it? A picture is worth a thousand words (and lest you think I cleaned up errors of mine in that whited out version, here's the original - I just didn't feel like fine tuning stuff to chop the file size in half).

P.S. "Grandmother's house" is either a helpful visual aid, or a red herring, depending on how you look at it. If, after reading the question, you find such a thing is never brought up again, merely use it as a frame of reference, but don't consider it in any of your equations (otherwise you might go down the wrong road [pun realized]). The problem could have merely said "Sam was due travelling due east, passed point a, and upon passing point b, was foo/bar from home/point a/point b. Upon passing point c, he was baz/xyzzy from point b, and foobar w.r.t. home and/or point a." Filling in the blanks is an exercise best left to the reader [Big Grin] .

P.P.S. I've been doing this math stuff for too long, haven't I? [Wink]

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There are three things you can be sure of in life: Death, taxes, and reading about fake illnesses online...

Posts: 9329 | From: Westchester County, New York | Registered: May 2001  |  IP: Logged
geekwannabebritt
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Icon 14 posted August 27, 2004 21:36      Profile for geekwannabebritt         Edit/Delete Post   Reply With Quote 
wow dragon! you really got into it!
thanks for your help [Big Grin]

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*/\~Brittney~/\*

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dragonman97

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Icon 1 posted August 27, 2004 21:47      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by geekwannabebritt:
wow dragon! you really got into it!
thanks for your help [Big Grin]

Eh, it was nothing - really. The top left sketch was the quick little thing I just took with me to the table, that pretty much set the stage for me, and bringing it to a QED* state didn't take terribly long. My description was just more verbose than that of the above posters - we all took the same exact process. To me, though, the process is more important than the end result in many cases - that is what is to be learned, not the precise answer. Knowing the answer gets one question done, knowing the process gets many more done, and builds a framework for future stuff.

Not to mention that it gave my brain a little bit of math exercise in problem solving, something I need to do a hell of a lot more of in prep. for taking the GRE...ugh.

*[Quite Easily Done [evil] [Wink] {please don't take this def. seriously if you don't know what it means}]

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There are three things you can be sure of in life: Death, taxes, and reading about fake illnesses online...

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Ivan
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Icon 1 posted August 28, 2004 14:54      Profile for Ivan   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Or you coulda done it in your head like me. Saved a napkin the horror of being marked on by a ball point pen.
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magefile
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Icon 1 posted September 07, 2004 17:33      Profile for magefile     Send New Private Message       Edit/Delete Post   Reply With Quote 
QED == quod erat demonstrandum == "which was to be done"

QEF == quod erat fundum (sp?) == "which was to be found"

Dragon: you mean the QEF point - quite easily figured (out) if you want a pun to go with it [Wink]

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quantumfluff
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Icon 1 posted September 07, 2004 20:16      Profile for quantumfluff     Send New Private Message       Edit/Delete Post   Reply With Quote 
If it were Mall of America, it would start 79 miles from his home and end 80 miles from his home.
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littlefish
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Icon 1 posted September 08, 2004 03:30      Profile for littlefish   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Help me solve one of these maths problems and we can be rich.
Posts: 2421 | From: That London | Registered: Nov 2001  |  IP: Logged
SimpleMan
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Icon 10 posted September 09, 2004 17:31      Profile for SimpleMan     Send New Private Message       Edit/Delete Post   Reply With Quote 
wow, (clap, clap, clap) I am gonna have to learn how to do all of that. You guys are just plain funny and on top of that made the problem look easy. Too funny. (clap, clap, clap) [Big Grin]

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Wrote a song bout it, like to hear it....here it go

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SimpleMan
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Icon 2 posted September 14, 2004 08:28      Profile for SimpleMan     Send New Private Message       Edit/Delete Post   Reply With Quote 
OK, I gotta know what gread math this is. I gave the problem to the math lab in my college and it has them scratching their heads. They did not get it yet and are still thinking about it. this goes to show you that just because you can help others with algebra and calculus....that they are not math masters. LOL I just think it is funny because here they are trying to be smart and help others with questions...can not do a word problem. [Big Grin]

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Wrote a song bout it, like to hear it....here it go

Posts: 47 | From: Virginia, USA | Registered: Jul 2004  |  IP: Logged
Stibbons
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Icon 1 posted September 14, 2004 08:51      Profile for Stibbons   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by magefile:
Dragon: you mean the QEF point - quite easily figured (out) if you want a pun to go with it [Wink]

Nah, the QED pun works too, because dman has proven dnf's/Ivan's work [Razz]

Have to agree with the dragon on the drawing pictures idea, it really helps to simplify many complex sounding mechanics and trig problems. Also if you're sitting an exams and have time at the end you can embelish the pictures, though it doesn't get you extra marks [Wink]

Posts: 1141 | From: UK | Registered: Dec 2003  |  IP: Logged


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