this is very OS dependent, so I will assume you are using win2K or XP type systems.
Also, I will assume that you don't care about the data on the (2) 10GB partitions.
The simple answer is to go into your storage manager (control panel-->Administrative tools-->computer manger-->[storage] -->[disk management]
there you will see all of your partitions. select the 10GB partitions and delete them, then select the 20GB unallocated space (this will be created after you delete the partitions) and create a new partition with that space...format it...and you are done.
If you want to do this the really easy, but not so free way, get acronis or partition magic. Acronis will do the partition work and even copy data from one partition to another for you.
By the way, what format is your backup image in? is it ghost? If it's a ghost image, you can use ghost to restore the data to the new partition.