Answer
The speed of the ship that passed you according to Earth observers is $0.97~c$
Work Step by Step
Let $v_{AE}$ be the velocity of ship A (our ship) relative to Earth. Then $v_{AE} = 0.90~c$
Let $v_{BA}$ be the velocity of ship B (the other ship) relative to ship A. Then $v_{BA} = 0.50~c$
We can find $v_{BE}$:
$v_{BE} = \frac{V_{BA}~+~v_{AE}}{1+\frac{(v_{BA})~(v_{AE})}{c^2}}$
$v_{BE} = \frac{(0.50~c)~+~(0.90~c)}{1+\frac{(0.50~c)~(0.90~c)}{c^2}}$
$v_{BE} = \frac{1.40~c}{1.45}$
$v_{BE} = 0.97~c$
The velocity of ship B relative to the Earth is $0.97~c$
Therefore, the speed of ship B relative to the Earth is $0.97~c$
