Answer
$R = 5.0~\Omega$
Work Step by Step
We can find the equivalent resistance of the circuit:
$R_{eq} = \frac{emf}{I}$
$R_{eq} = \frac{93.5~V}{17~A}$
$R_{eq} = 5.5~\Omega$
Note that: $~5.5~\Omega - 4.0~\Omega = 1.5~\Omega$
We can find the value of $R$:
$\frac{1}{1.5} = \frac{1}{2.0}+\frac{1}{R+1.0}$
$\frac{1}{1.5} - \frac{1}{2.0}=\frac{1}{R+1.0}$
$\frac{1}{6.0}=\frac{1}{R+1.0}$
$6.0 = R+1.0$
$R = 5.0~\Omega$
