Answer
The plane that flew east flew at $300$ miles per hour while the other plane flew at a speed of $600$ miles per hour.
Work Step by Step
Let $x$ be the speed of the slower plane going east in miles per hour.
$2x$ is the speed of the plane going west.
Recall that:
Speed$\times$time$=$distance
If they are $2700$ miles apart after $3$ hours then,
$3x+2x(3)=2700$
$3x+6x=2700$
$9x=2700$
$x=300$
So, the faster plane flew at $600$miles per hour.
