Statement (1) alone:
This tells us that Bob and Nancy travel together for at least part of their commute. However, it doesn't provide any information about the total duration of their commutes or whether their entire commutes are identical. We don't know if one of them continues traveling after they separate.
Therefore, this statement alone is not sufficient.
Statement (2) alone:
This tells us when Nancy and Bob arrive at their respective offices relative to each other. However, it doesn't provide any information about when they started their commutes. Nancy could have a longer commute but leave earlier, or have a shorter commute but leave later.
Therefore, this statement alone is not sufficient.
Statements (1) and (2) together:
We know they travel together for part of their commute.
We also know Nancy arrives at her office 5 minutes before Bob.
However, we still don't know:
- If their entire commutes are identical except for the last 5 minutes.
- If one of them has additional travel time before or after their shared train ride.
Even with both statements, we can't determine whose total commute time is longer.
Therefore, the correct answer is (E): Both statements together are insufficient.