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DarkBlueChocobo

  • one year ago

Help with application problem

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  1. DarkBlueChocobo
    • one year ago
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    Your college quadrangle is 85 meters long and 66 meters wide. When you are late for class, you can walk at 7 miles per hour. You are at one corner of the quad and your class is directly opposite corner. How much time can you save by cutting across rather than going around the edge.

  2. DarkBlueChocobo
    • one year ago
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    So i sketched it out

  3. SolomonZelman
    • one year ago
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    Pythagorean Theorem

  4. DarkBlueChocobo
    • one year ago
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    |dw:1443659413569:dw|

  5. DarkBlueChocobo
    • one year ago
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    85^2+66^2=x^2 sqrt11581 = x 107.6=x

  6. DarkBlueChocobo
    • one year ago
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    So in order to find how much time it saves we have to change 7 miles per hour to 6 meters per hour?

  7. SolomonZelman
    • one year ago
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    Yes, that is the distance which you cut accross. Now, how much distance does save you? You would have walked 85+66 without cutting, so subtract *(85+66) - √[88²+65²]*

  8. DarkBlueChocobo
    • one year ago
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    how many meters***

  9. DarkBlueChocobo
    • one year ago
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    not 6

  10. SolomonZelman
    • one year ago
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    this in bold is the distance travelled in miles, and then divide by 7 to find the number of hours saved.

  11. SolomonZelman
    • one year ago
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    http://www.wolframalpha.com/input/?i=%28%2885%2B65%29-%E2%88%9A%2888%C2%B2%2B65%C2%B2%29%29%2F7 yes just a bit less than 6

  12. DarkBlueChocobo
    • one year ago
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    So 5.799 hours saved?

  13. SolomonZelman
    • one year ago
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    Yes.

  14. SolomonZelman
    • one year ago
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    (If you would like we can do a by-hand approximation (I mean Taylor Polynomial) of the square root.....)

  15. DarkBlueChocobo
    • one year ago
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    Wells this is an example problem from my engineering textbook. Was just wondering how to get the time saved, but why do we do *(85+66) - √[88²+65²]*

  16. DarkBlueChocobo
    • one year ago
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    is it because 88+66 is the walking around the corner

  17. DarkBlueChocobo
    • one year ago
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    and sqrt88^2+65^2 is the cut through? Also why do we square this?

  18. SolomonZelman
    • one year ago
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    well, (85+66) miles is the distance that takes you to walk without cuttting across, correct?

  19. DarkBlueChocobo
    • one year ago
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    Yes

  20. SolomonZelman
    • one year ago
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    And *√[88²+65²] miles* is the distance that takes you when you cut across.

  21. SolomonZelman
    • one year ago
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    So, the distance you saved by walking across is (85+66) - √[88²+65²]

  22. DarkBlueChocobo
    • one year ago
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    wait also where did the 88 come from?

  23. SolomonZelman
    • one year ago
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    Oh, typo

  24. SolomonZelman
    • one year ago
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    I apologize

  25. SolomonZelman
    • one year ago
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    88 should be 85

  26. DarkBlueChocobo
    • one year ago
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    so that means that the hours saved would be 6.285

  27. SolomonZelman
    • one year ago
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    When you cut, you walk: *√[85²+66²] miles* Without cutting across *(85+66) miles* And then *(85+66) - √[85²+66²] miles* is the distance that you have saved by cutting across. THEN, the time your have saved [knowing that you walk 7 miles per hour] *( (85+66) - √[85²+66²] ) / 7*

  28. DarkBlueChocobo
    • one year ago
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    Alright That makes a lot more sense putting it that way

  29. SolomonZelman
    • one year ago
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    6.19784932

  30. SolomonZelman
    • one year ago
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    yw

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