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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

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

so, substituting your data we get: $\Large 2700 = 3{v_A} \times 3$ please solve for v_A

3. anonymous

wait what?

4. anonymous

can u explain please

5. Michele_Laino

we have: $\Large 2700 = 9{v_A}$

6. Michele_Laino

now, please divide both sides by 9, what do you get?

7. Michele_Laino

hint: |dw:1434807331602:dw| what is v_A?

8. Plasmataco

YAY!

9. anonymous

is it 900?

10. Michele_Laino

it is: $\Large {v_A} = 300\;{\text{miles/hours}}$

11. anonymous

what about the other plane? I know it's 600 but how do we know it's 600?

12. Michele_Laino

since v_B is twice of v_A: $\Large {v_B} = 2{v_A} = 2 \times 300 = ...{\text{miles/hours}}$

13. anonymous

ohhhhhhhh

14. anonymous

so what is the algebraic equation for this?

15. Michele_Laino

the algebraic equations which models your problems are: $\Large \left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.$

16. anonymous

what is all that mumbo jumbo??????? I know Distance = Time x Speed

17. Michele_Laino

the equation which model your problem are:

18. Michele_Laino

$\left\{ \begin{gathered} d = {v_A}t + {v_B}t \hfill \\ {v_B} = 2{v_A} \hfill \\ \end{gathered} \right.$

19. Michele_Laino

so the algebraic equation for v_B, is: $\Large {v_B} = 2{v_A}$

20. Michele_Laino

the relative distance d between the planes is given by this function: $\Large d\left( t \right) = \left( {{v_A} + {v_B}} \right)t$

21. Michele_Laino

since the distance d depends on the elapsed time t

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