Answer
The speed of Baker relative to the Earth observer is $0.300~c$
Work Step by Step
Let $v_{BA}$ be the velocity of Baker relative to Able. Then $v_{BA} = -0.114~c$
Let $v_{AE}$ be the velocity of Able relative to Earth. Then $v_{AE} = 0.400~c$
We can find $v_{BE}$:
$v_{BE} = \frac{V_{BA}~+~v_{AE}}{1+\frac{(v_{BA})~(v_{AE})}{c^2}}$
$v_{BE} = \frac{(-0.114~c)~+~(0.400~c)}{1+\frac{(-0.114~c)~(0.400~c)}{c^2}}$
$v_{BE} = \frac{0.286~c}{0.9544}$
$v_{BE} = 0.300~c$
The velocity of Baker relative to the Earth is $0.300~c$
Therefore, the speed of Baker relative to the Earth observer is $0.300~c$.
