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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 09:43 AM
Original message
DuStrange's Math Problem of the Day.
As many of you may know, MrCoffee lives near a hill. And every weekend, he runs from his house to the foot of the hill, then up to the top of the hill, back to the bottom, and then back home. Now, the distance from his house to the top of the hill is 6 miles. MrCoffee can run 3 mph along a flat surface, 2 mph when he is running uphill, and then 6 mph when he is running downhill.

So, once he leaves his house, how long does it take for him to return home?



The winner gets this fully functional Transformers costume:


Offer void in states which have land.
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ProfessorGAC Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 09:48 AM
Response to Original message
1. 2 MPH is Running?
Geez, i have MS and can move faster than that!
The Professor
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:05 AM
Response to Reply #1
9. Please, let's not embarrass MrCoffee.
His ego bruises easily.
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TZ Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 09:55 AM
Response to Original message
2. You are asking me to do a math WORD PROBLEM
on a Monday morning? You crazy dude.... :crazy:
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:21 AM
Response to Reply #2
17. You will do it...
and you will enjoy it!

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DS1 Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 09:57 AM
Response to Original message
3. You don't specify the distance from the house to the hill
so the question cannot be answered.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:09 AM
Response to Reply #3
11. I did not specify the distance from the house to the hill...
and yet the question can still be answered.

Do not underestimate the power of mathematics.
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redqueen Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 09:59 AM
Response to Original message
4. What's the distance from his house
to the bottom of the hill?

That's a big hill.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:15 AM
Response to Reply #4
15. Call it x.
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siligut Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 10:00 AM
Response to Original message
5. Running downhill can ruin the knees!
Tell him not to run downhill, he will regret it later in life.
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Nye Bevan Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 10:42 AM
Response to Original message
6. 4 hours (nt)
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:08 AM
Response to Reply #6
10. WINNER!
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kath Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:37 AM
Response to Reply #6
22. Cool! Good job!
Turns out that,since you know the total distance and all of the rates involved, you don't need to know how the distance is divided up in order to solve for the total time.

(we homeschool, and since I've spent a fair amount of time helping my kids with math, all (or at least most ;-) ) of that high school algebra has come back to me.)
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Parche Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 10:45 AM
Response to Original message
7. He Takes The Bus
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Pierre.Suave Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 10:47 AM
Response to Original message
8. Dust Range gets an F today
because he did not include how far MrCoffee lives from the base of the hill.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:12 AM
Response to Reply #8
13. jasonc gets an F for the WHOLE week!
For not recognizing that the distance is irrelevant.

You also win this hat.

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Pierre.Suave Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:20 AM
Response to Reply #13
16. If he has to travel that distance
how can it not matter?
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:22 AM
Response to Reply #16
18. Do the math!
I'm begging you.

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Tuesday Afternoon Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:09 AM
Response to Original message
12. hey...thanks for the costume idea
I could be wrong but, I don't think there is enough info given in the word problem :shrug:
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:14 AM
Response to Reply #12
14. You are wrong.
Your punishment is to write a 7-page essay on the impact of the harmonic mean on Supreme Court decisions.
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Tuesday Afternoon Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:24 AM
Response to Reply #14
19. alrighty then...
but, it all boils down to living in harmony with all that surrounds us. Simply put:

Live simply so that others may simply live.

:yoiks:
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rug Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:31 AM
Response to Original message
20. 17.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:36 AM
Response to Reply #20
21. No!
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rug Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:39 AM
Response to Reply #21
23. Crap.
:cry:
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Rabrrrrrr Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:41 AM
Response to Original message
24. Because of the speeds you chose, one can ignore slope and consider it all flat - 4 hours.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:43 AM
Response to Reply #24
26. Excellent!
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SOteric Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:41 AM
Response to Original message
25. Let's see...
Factoring in the 7 minutes each spent at 6 stoplights, prancing, stretching and running in place; and allowing for the 4 minute spontaneous stretch that occurred just as a pretty blonde in running shorts passed by; calculating the 17.25 minutes it took MrCoffee to feign a heart attack going uphill in hopes that same pretty blonde would offer mouth to mouth; and now allowing for the 3.25 hours he spent under Mrs. Finklesteen's rose hedge on the way down, where first he fell, then he was held at bay by the neighbour's aggressive Doberman, and where finally he ended up taking a nice little nap...

*pencil scritching* ....carry the one...

MrCoffee requires 7 hours, 22 minutes and 57 seconds to carry out his weekly run.**










**Margin for error + or - 7 hrs, 22 minutes and 57 seconds.
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:45 AM
Response to Reply #25
27. Serves me right for using MrCoffee as my subject.
Nonetheless, your story was immensely pleasing.

:rofl:
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MrCoffee Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 01:07 PM
Response to Reply #25
35. :thumbsup:
Win.
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motely36 Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:15 PM
Response to Original message
28. Please explain for the algebra impaired
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:28 PM
Response to Reply #28
29. Okay, it's like this.
If we let x be the distance from his house to the bottom of the hill, then the distance from the bottom of the hill to the top is 6-x. So, we use the formula "time = distance / rate" to find the amount of time it takes to run each part.
From the house to the bottom of the hill: x/3
Up the hill: (6-x)/2
Down the hill: (6-x)/6
From the bottom of the hill back to the house: x/3.
Adding these together, we get
x/3 + (6-x)/2 + (6-x)/6 + x/3 = (2x + 18 - 3x + 6 - x + 2x)/6 = 24/6 = 4.
So it takes four hours, and the value of x is irrelevant.

It turns out that x is irrelevant because the harmonic mean of the uphill and downhill speeds (2 and 6) is equal to the flat surface speed (3).
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motely36 Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:33 PM
Response to Reply #29
31. got it!
and learned something new.
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SOteric Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:35 PM
Response to Reply #29
32. You forgot
xx where xx represents the chromosome count of the pretty blonde in running shorts.
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tosh Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:32 PM
Response to Original message
30. That Transformer costume is making me dizzy.
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radfringe Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:45 PM
Response to Original message
33. I know... ohh ohhh I know
takes him about an hour, because he catches the train that left the station traveling west at 50 mph
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Dr. Strange Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 12:50 PM
Response to Reply #33
34. I think you need to spend more time reading your textbook:
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DarkTirade Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 10:36 PM
Response to Original message
36. Depending on how good his health insurance is, after he collapses from exhaustion
the hospital might kick him out after a few hours, or they might keep him overnight for observation.
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Hosnon Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Oct-27-08 11:49 PM
Response to Original message
37. Hmm...I just assumed the hill had no height and got 4.
Edited on Mon Oct-27-08 11:52 PM by MJDuncan1982
Looks like it only worked because of the ratio between the uphill and downhill speeds.

Edit: Yeah, what Rabrrr said.
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