Some times it is common for 2 or 3 planes to take off really close to each other while a plane is final.
Ex.
A few years ago there was a Learjet on approach at Orange County (SNA), and the tower cleared an Alaska 737 for immidiate take off. While the Alaska was lining up, another Alaska told the tower that they were ready. The Learjet was now at 4 miles, and the tower told the second Alaska that if they knew they could take off quickly they could go. The 2nd Alaska said they could and just as the 1st Alaska took off, the 2nd Alaska released the brakes and was off 18 seconds before the Learjet landed. I knew it was 18 second because I timed it:
So, in short, it's common