anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
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|
Michele_Laino
  • Michele_Laino
so, substituting your data we get: \[\Large 2700 = 3{v_A} \times 3\] please solve for v_A
anonymous
  • anonymous
wait what?

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anonymous
  • anonymous
can u explain please
Michele_Laino
  • Michele_Laino
we have: \[\Large 2700 = 9{v_A}\]
Michele_Laino
  • Michele_Laino
now, please divide both sides by 9, what do you get?
Michele_Laino
  • Michele_Laino
hint: |dw:1434807331602:dw| what is v_A?
Plasmataco
  • Plasmataco
YAY!
anonymous
  • anonymous
is it 900?
Michele_Laino
  • Michele_Laino
it is: \[\Large {v_A} = 300\;{\text{miles/hours}}\]
anonymous
  • anonymous
what about the other plane? I know it's 600 but how do we know it's 600?
Michele_Laino
  • Michele_Laino
since v_B is twice of v_A: \[\Large {v_B} = 2{v_A} = 2 \times 300 = ...{\text{miles/hours}}\]
anonymous
  • anonymous
ohhhhhhhh
anonymous
  • anonymous
so what is the algebraic equation for this?
Michele_Laino
  • Michele_Laino
the algebraic equations which models your problems are: \[\Large \left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.\]
anonymous
  • anonymous
what is all that mumbo jumbo??????? I know Distance = Time x Speed
Michele_Laino
  • Michele_Laino
the equation which model your problem are:
Michele_Laino
  • Michele_Laino
\[\left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.\]
Michele_Laino
  • Michele_Laino
so the algebraic equation for v_B, is: \[\Large {v_B} = 2{v_A}\]
Michele_Laino
  • Michele_Laino
the relative distance d between the planes is given by this function: \[\Large d\left( t \right) = \left( {{v_A} + {v_B}} \right)t\]
Michele_Laino
  • Michele_Laino
since the distance d depends on the elapsed time t

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