It depends on the firm that you are choosing. If that software designing and developing firm are just newbie then it will take lot of time. Apart from that choose well experienced firm and it will take less amount of time.
if i were to guess i'd guess forever? a full army at google took lightyears to release google +. what makes you think a freelancer will do it in any less time?
There are two points to consider:
1) Do you have a full scope, description, etc. to help a development company come up with something? The reason why I ask, most development companies will not do carte blanche development except to say $X per hour and be ready to cut checks at milestones.
2) What is your budget? If you are wanting what I think you do, it can be done for a few thousand. But if you are wanting all this for about $200, you're dreaming. Reputable companies will charge a nominal price. Dirt cheap will show you the quality of development and/or the support.
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