Am in real need of some help here!

My wife hired out a Ford Focus diesel yesterday to go on a long trip. Well she is back but she has just found out that she cant find the key fob thing that needs to be in your hand to start the car as it is push button start. We have turned the car inside out and still cant find it! What is the radios on these keys as it maybe in the house.....House is about 15ft from the car. The car is still starting though and I drove it about 600-700 yards down the road and pulled over, pushed the button to stop the car, left it about 1 minute then pushed the button again and it started??!!

I am dreading that we wont be able to find it as the car has to be back tomorrow morning and the hire car company will charge some stupid amount for a new key fob thing.

Any help on...... 'Does the key need to be within a certain distance and how far is that distance to start the car' would be great.