The Application Process

I was wondering if any one out there might be able to help with a dilemma I'm currently having. I've applied to executive MBA programmes at two well-ranked UK business schools. I successfully got through the first part of the application process, and was recently invited to interview at both schools.

Earlier today I received an offer from one of these schools saying that they would be pleased to offer me a place. I am of course delighted by this outcome. However, this offer is from my back-up choice, and the one I'm really holding out for have yet to make a decision. I expect to hear from this other school towards the end of this week/early next week.

I really should send an acknowledgement to the school that has made the offer, but I wanted to hold off on a final decision until I have heard definitively from the other school.

Any ideas how to best approach this? Is it worth contacting the other school and enquiring whether they are able to accelerate their process?

I definitely don't want to create any bad feeling with either school, or shoot myself in the foot with the current offer.

Any ideas would be gratefully received!