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Grazes Group Title

Joe rides his bike to his friend Jon's house and returns home by the same route. Joe rides his bike at constant speeds of 6 , on level ground, 4 mph when going uphill, and 12 mph when going downhill. If his total time riding was 1 hour, how far is it to Jon's house?

  • 2 years ago
  • 2 years ago

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  1. satellite73 Group Title
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    my guess is 3 miles but i could be wrong

    • 2 years ago
  2. satellite73 Group Title
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    yes i believe 3 miles is the right answer

    • 2 years ago
  3. satellite73 Group Title
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    first off, since you are not told how many miles are uphill, downhill or flat, it cannot matter since it doesn't matter we can assume that it is all flat, and that it took him 1 hour going 6 mph to get there and back, so his total trip was 6 miles and half of it is 3

    • 2 years ago
  4. satellite73 Group Title
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    suppose on the other hand that it is uphill all the way there. then it is downhill all the way back his travel time there is \(\frac{D}{4}\) and back it will be \(\frac{D}{12}\) and the total is 1 hour. solve \[\frac{D}{4}+\frac{D}{12}=1\] and you still get \(D=3\)

    • 2 years ago
  5. satellite73 Group Title
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    cute question though isn't it?

    • 2 years ago
  6. Grazes Group Title
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    According to the textbook, it is 3 miles.

    • 2 years ago
  7. Grazes Group Title
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    I'm not so sure about cute, though

    • 2 years ago
  8. satellite73 Group Title
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    yes that is what i got as well

    • 2 years ago
  9. satellite73 Group Title
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    point being that he averages 6 mph no matter what portion is up, down or flat

    • 2 years ago
  10. satellite73 Group Title
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    we can probably prove that without much difficulty

    • 2 years ago
  11. Grazes Group Title
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    Just one thing. Why wouldn't you add the work rate of 6mph in? : \[\frac{ D }{ 4 }+\frac{ D }{ 6 }+\frac{ D }{ 12 }=1\]

    • 2 years ago
  12. satellite73 Group Title
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    what does D represent in your equation? in mine it is the distance form one house to the other

    • 2 years ago
  13. satellite73 Group Title
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    if it is all flat, it is a constant rate of 6 mile per hour, so the distance is 3 miles,

    • 2 years ago
  14. Grazes Group Title
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    I thought of it as a work problem. So the rates would equal the work rates and the D would be time

    • 2 years ago
  15. Grazes Group Title
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    oh wait.... D is the distance and the time is the 1

    • 2 years ago
  16. satellite73 Group Title
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    you lost me there this problem is about distance, rate and time i would put D = distance between the houses, because that is what you need to solve for

    • 2 years ago
  17. satellite73 Group Title
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    lets prove that no matter what part is flat, up or down, he travels at an average rate of 6 mph

    • 2 years ago
  18. satellite73 Group Title
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    clearly he averages 6 mph on the flat part, because that is what is says now suppose \(x\) miles are uphill going then returning those same \(x\) miles are downhill the rate uphill is \(4\) so the time uphill is \(\frac{x}{4}\) and the rate downhill is \(12\) so the time downhill is \(\frac{x}{12}\) the total time is for those parts are therefore \(\frac{x}{4}+\frac{x}{12}=\frac{x}{3}\) and the total distance travelled is \(2x\) therefor the average speed is \(\frac{2x}{\frac{x}{3}}=6\)

    • 2 years ago
  19. satellite73 Group Title
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    meaning no matter what portion is up, down or flat, his average rate is 6 mph but all this is really extra work since you are not told what portion is up down or flat, it makes no difference if it makes no difference, assume that it is all flat and you get 3 right away

    • 2 years ago
  20. Grazes Group Title
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    I guess.

    • 2 years ago
  21. satellite73 Group Title
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    for sure, good trick to remember if you are taking a standardized test and have to answer quickly if you are not told a number you think you need make up one and work with that since we were not told what portion of the trip was flat, i made it all flat

    • 2 years ago
  22. Grazes Group Title
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    lol.

    • 2 years ago
  23. Grazes Group Title
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    Thanks.

    • 2 years ago
  24. satellite73 Group Title
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    yw

    • 2 years ago
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