A CRJ-900 Flight Crew; distracted by ancillary duties and non work related problems; failed to slow to 250 KTS as assigned by ATC. A further speed restriction was required to avoid separation issues.

Narrative

We were given the clearance to cross SHINE intersection at 250 KTS and 12;000 FT. After SHINE the Controller asked for our speed and if we had been given a speed restriction. I had been off line getting a gate assignment and doing the passenger brief and came back on the frequency just as the Controller asked our speed; impulsively and without checking I responded 250. In reality we were going faster than the 250 restriction. The Controller said 'really?' and asked the air carrier aircraft ahead how fast they were going. The Controller then told us we were going 50 KTS faster; over taking and to slow to 210.I felt bad that I wasn't more attentive and asked the Captain about the speed issue. He felt bad too and admitted that he was distracted about problems outside of work. After we were handed off; the Captain asked the new Controller for a phone number to Approach Control. He called the number after we stopped at the gate and apologized for going too fast after SHINE.Cause: Distractions due to other non-flying duties and problems outside of work. Prevention: Obviously; more attentiveness. Aircraft with FMS systems should be required to have the ATIS; gate assignments etc. transmitted electronically into the FMS. This would keep both pilots inside the cockpit and focused on the flying.