Consider two metallic rods mounted on insulated supports. One is neutral, another positively charged. The charged rod is brought close to the neutral one (no touching!) and at this time the neutral rod was briefly grounded (for instance, touched by your hand).

Part (a) What would be resulting charge (if any) on initially neutral rod?

1) There is not enough information given to be able to answer.
2) It will be positively charged.
3) It will be negatively charged.
4) It will remains neutral.

The resulting charge on the initially neutral rod will be  3.) it will be negatively charged.

Explanation:

If the neutral rod is brought close to the neutral one and if the neutral rod is touching the ground then the positive charges will attract electrons from the ground on to the rod.

The Earth (or ground) has electrons in abundance and electrons can be taken from of fed into the Earth without having any significant impact on the Earth's electric field.

So. the resulting charge on the initially neutral rod will be  3.) it will be negatively charged.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)