Hey there, kingicev!
Yes, they shouldn't have any issues working together. However, in the RAID 1, the 15K.7 would be bottlenecked by the 10K.7 drive. In other words, it would have the performance of your slowest HDD in the RAID configuration. I'd also suggest you to make sure that their capacities match at least so that you'd not bottleneck the storage space as well. Generally speaking, you need to match them in terms of Speed, Capacity, Manufacturer & Model. Afterwards, you shouldn't encounter any issues rebuilding the array.
P.S. Always make sure you have the RAID backed up elsewhere as well. Even RAID 1 cannot be considered a backup solution. Multiple copies of your data is what will save you from data loss at the end of the...