DuStrange's Math Problem of the Day.

[Dr. Strange]

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.

[ProfessorGAC]

1. 2 MPH is Running?

Geez, i have MS and can move faster than that!
The Professor

[Dr. Strange]

9. Please, let's not embarrass MrCoffee.

His ego bruises easily.

[TZ]

2. You are asking me to do a math WORD PROBLEM

on a Monday morning? You crazy dude....:crazy:

[Dr. Strange]

17. You will do it...

and you will enjoy it!

[DS1]

3. You don't specify the distance from the house to the hill

so the question cannot be answered.

[Dr. Strange]

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.

[redqueen]

4. What's the distance from his house

to the bottom of the hill?

That's a big hill.

[Dr. Strange]

15. Call it x.

[siligut]

5. Running downhill can ruin the knees!

Tell him not to run downhill, he will regret it later in life.

[Nye Bevan]

6. 4 hours (nt)

[Dr. Strange]

10. WINNER!

[kath]

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.)

[Parche]

7. He Takes The Bus

[Pierre.Suave]

8. Dust Range gets an F today

because he did not include how far MrCoffee lives from the base of the hill.

[Dr. Strange]

13. jasonc gets an F for the WHOLE week!

For not recognizing that the distance is irrelevant.

You also win this hat.

[Pierre.Suave]

16. If he has to travel that distance

how can it not matter?

[Dr. Strange]

18. Do the math!

I'm begging you.

[Tuesday Afternoon]

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:

[Dr. Strange]

14. You are wrong.

Your punishment is to write a 7-page essay on the impact of the harmonic mean on Supreme Court decisions.

[Tuesday Afternoon]

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:

[rug]

20. 17.

[Dr. Strange]

21. No!

[rug]

23. Crap.

:cry:

[Rabrrrrrr]

24. Because of the speeds you chose, one can ignore slope and consider it all flat - 4 hours.

[Dr. Strange]

26. Excellent!

[SOteric]

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.

[Dr. Strange]

27. Serves me right for using MrCoffee as my subject.

Nonetheless, your story was immensely pleasing.

:rofl:

[MrCoffee]

35. :thumbsup:

Win.

[motely36]

28. Please explain for the algebra impaired

[Dr. Strange]

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).

[motely36]

31. got it!

and learned something new.

[SOteric]

32. You forgot

xx where xx represents the chromosome count of the pretty blonde in running shorts.

[tosh]

30. That Transformer costume is making me dizzy.

[radfringe]

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

[Dr. Strange]

34. I think you need to spend more time reading your textbook:

[DarkTirade]

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.

[Hosnon]

37. Hmm...I just assumed the hill had no height and got 4.

Looks like it only worked because of the ratio between the uphill and downhill speeds.

Edit: Yeah, what Rabrrr said.