Spiderman vs Batman, but not at fighting

Both of them are isekai into a replica Earth which have no superheroes/villains and are trying to get back home.

The rules:

• They are standard version and only have standard gear that they always carry on them (no hellbat, throne, power cosmic, symbiote etc ...)

• Spiderman will assume the identity of Peter Parker, a random college student.

• Batman will assume the identity of Bruce Wayne, a small business owner.

• Both have 100k in assets/money.

• The world is peaceful, and law abiding, and they do not like superhero vigilantes. The police would try to capture the anyone who tried to take justice to their own hand. The police there is competent by comic book standard.

• Their target is a mage who is adept in disguised and have a public identity. His minor experiment gone wrong and result in the isekai of the two heroes, and they are trying to get back home. He is as competent as Dr.Strange/Fate, but not at combat, and would not hurt people.

Which of the heroes would manage to return home first?