Understanding the Problem
To determine how long B will take to complete the work alone, we first need to analyze the work rates of A and B based on the information provided.

Work Rates of A and B
- A and B together can complete the work in 35 days.
- Therefore, their combined work rate is:
\[
\text{Work Rate of (A + B)} = \frac{1}{35} \text{ (work/day)}
\]
- A alone can complete the work in 60 days.
- Thus, A's work rate is:
\[
\text{Work Rate of A} = \frac{1}{60} \text{ (work/day)}
\]

Calculating B's Work Rate
To find B's work rate, we can use the combined work rate:
- The equation for their combined work rate is:
\[
\text{Work Rate of A} + \text{Work Rate of B} = \text{Work Rate of (A + B)}
\]
- Substituting the known values:
\[
\frac{1}{60} + \text{Work Rate of B} = \frac{1}{35}
\]
- To isolate B's work rate, we rearrange the equation:
\[
\text{Work Rate of B} = \frac{1}{35} - \frac{1}{60}
\]

Finding a Common Denominator
- The least common multiple of 35 and 60 is 420.
- Converting the fractions:
\[
\frac{1}{35} = \frac{12}{420} \quad \text{and} \quad \frac{1}{60} = \frac{7}{420}
\]
- Thus:
\[
\text{Work Rate of B} = \frac{12}{420} - \frac{7}{420} = \frac{5}{420} = \frac{1}{84}
\]

Calculating B's Time to Complete Work Alone
- If B's work rate is \(\frac{1}{84}\), then the time taken by B to complete the work alone is:
\[
\text{Time} = \frac{1}{\text{Work Rate of B}} = 84 \text{ days}
\]

Conclusion
B alone will be able to complete the work in **84 days**.