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anonymous

  • one year ago

two planes left an airport at noon, one flew east and the other flew west at twice the speed. After 3 hours the planes were 2700mi apart. How fast was each plane flying?

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  1. Michele_Laino
    • one year ago
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    I call with v_A and v_B the velocities of each plane say plane A and plane B, furthermore, be: v_B=2*v_A then we can write: \[\Large d = {v_A}t + {v_B}t = {v_A}t + 2{v_A}t = 3{v_A}t\] where t is the time namely t= 3 hours, and d is their separation, namely d= 2,700 mi |dw:1434806880955:dw|

  2. Michele_Laino
    • one year ago
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    so, substituting your data we get: \[\Large 2700 = 3{v_A} \times 3\] please solve for v_A

  3. anonymous
    • one year ago
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    wait what?

  4. anonymous
    • one year ago
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    can u explain please

  5. Michele_Laino
    • one year ago
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    we have: \[\Large 2700 = 9{v_A}\]

  6. Michele_Laino
    • one year ago
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    now, please divide both sides by 9, what do you get?

  7. Michele_Laino
    • one year ago
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    hint: |dw:1434807331602:dw| what is v_A?

  8. Plasmataco
    • one year ago
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    YAY!

  9. anonymous
    • one year ago
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    is it 900?

  10. Michele_Laino
    • one year ago
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    it is: \[\Large {v_A} = 300\;{\text{miles/hours}}\]

  11. anonymous
    • one year ago
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    what about the other plane? I know it's 600 but how do we know it's 600?

  12. Michele_Laino
    • one year ago
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    since v_B is twice of v_A: \[\Large {v_B} = 2{v_A} = 2 \times 300 = ...{\text{miles/hours}}\]

  13. anonymous
    • one year ago
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    ohhhhhhhh

  14. anonymous
    • one year ago
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    so what is the algebraic equation for this?

  15. Michele_Laino
    • one year ago
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    the algebraic equations which models your problems are: \[\Large \left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.\]

  16. anonymous
    • one year ago
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    what is all that mumbo jumbo??????? I know Distance = Time x Speed

  17. Michele_Laino
    • one year ago
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    the equation which model your problem are:

  18. Michele_Laino
    • one year ago
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    \[\left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.\]

  19. Michele_Laino
    • one year ago
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    so the algebraic equation for v_B, is: \[\Large {v_B} = 2{v_A}\]

  20. Michele_Laino
    • one year ago
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    the relative distance d between the planes is given by this function: \[\Large d\left( t \right) = \left( {{v_A} + {v_B}} \right)t\]

  21. Michele_Laino
    • one year ago
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    since the distance d depends on the elapsed time t

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