Let's solve the equations step-by-step.
We start with:
- \( s = 4b \)
- \( s + b = 55 \)
Substituting the value of \( s \) from the first equation into the second equation:
\[ 4b + b = 55 \]
This simplifies to:
\[ 5b = 55 \]
Now, divide both sides by 5 to solve for \( b \):
\[ b = \frac{55}{5} = 11 \]
Thus, the value of \( b \) is \( \boxed{11} \).