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anonymous

  • 5 years ago

During the first part of a trip, a conoeist travels 34 miles at a certain speed. The conoeist travels 6 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?

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  1. anonymous
    • 5 years ago
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    yeh, its very similar to all questions asked one use pronumerals to represent unknowns

  2. anonymous
    • 5 years ago
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    let the first speed be x

  3. anonymous
    • 5 years ago
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    then distance = rate x time

  4. anonymous
    • 5 years ago
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    time = distance/rate

  5. anonymous
    • 5 years ago
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    time for first section of trip is T1 = 34/x now, the speed they travel for second part of trip is (x-5) { 5mph slower} so time for second part = T2 = 6/ (x-5) and we are told that the total trip = 3hrs so the sum of the times = 3hrs

  6. anonymous
    • 5 years ago
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    \[\frac{34}{x} + \frac{6}{x-5} = 3\]

  7. anonymous
    • 5 years ago
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    solve for x,

  8. anonymous
    • 5 years ago
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    this gives 2 solutions x= 3.94 and x= 14.4

  9. anonymous
    • 5 years ago
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    now, the answer cannot be x=3.94 , because if we try to determine the speed of the second part of the trip then we would get a negative value ( remember the speed for second trip was (x-5)mph )

  10. anonymous
    • 5 years ago
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    therefore x=14.4mph is the speed for first section , and 9.4mph is the speed for the second section

  11. anonymous
    • 5 years ago
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    \[\sqrt{9x+67}=x+5\]

  12. anonymous
    • 5 years ago
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    what ?

  13. anonymous
    • 5 years ago
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    I need to solve....well see what the heck I did wrong anyway..

  14. anonymous
    • 5 years ago
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    then I have one more..if that is ok...then I will leave everyone alone...I hate that I get so confused

  15. anonymous
    • 5 years ago
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    square both sides 9x + 67 = x^2 +10x +25 x^2 +x +25-67 =0 x^2 + x -42=0 (x+7)(x-6) =0

  16. anonymous
    • 5 years ago
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    x=6, x=-7 but check your solns

  17. anonymous
    • 5 years ago
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    x=-7 doesnt work, so x=6 is only soln

  18. anonymous
    • 5 years ago
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    ok so one more if you have time?

  19. anonymous
    • 5 years ago
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    might as well, shouldnt take long

  20. anonymous
    • 5 years ago
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    Write a quadratic equation in the variable x having the given numbers as solutions. The equation is standard form, ax^2+bx+c=0 \[-\sqrt{3}, 6\sqrt{3}\]

  21. anonymous
    • 5 years ago
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    \[(x+\sqrt{3}) ( x-6\sqrt{3}) =0\]

  22. anonymous
    • 5 years ago
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    expand

  23. anonymous
    • 5 years ago
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    x^2 -6sqrt(3)x +sqrt(3)x -6sqrt(3)sqrt(3) =0 \[x^2 - 6\sqrt{3}x - 18 =0 \]

  24. anonymous
    • 5 years ago
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    wait no

  25. anonymous
    • 5 years ago
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    \[x^2 -5\sqrt{3}x -18 =0 \] thats it

  26. anonymous
    • 5 years ago
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    if you have a quadratic eqn with roots a and b , then the formula for that quadratic is (x-a)(x-b) =0

  27. anonymous
    • 5 years ago
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    ok..thanks:)

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