1:40 with hand baggage only is probably just about do-able - it's about a 25 minute bus ride, and allowing 10 mins in case you miss one etc - though I'm sure the EDI locals will be along shortly with a traffic and travel report about the latest impact of the tram works in Edinburgh...

We'll move this over to UK & Ireland, where you'll find similar discussions and some cathartic stress relief threads about said tram works