B757-200
Flight Crew Air Transport Pilot (ATP)
Time Pressure; Workload
Aircraft Equipment Problem Critical; Inflight Event / Encounter Fuel Issue
Flight Crew Overcame Equipment Problem
Aircraft
Upon passing FL250 climbing to FL350 the cabin altitude began to climb between 700 feet minimum to 1;000 feet minute. Once the cabin altitude reached approximately 8;000 feet we stopped the climb and requested a descent to 10;000 feet. I used the expedited descent procedures and descended to 10;000 feet without letting the cabin altitude increase above 10;000 feet. At this point I ran fuel calculations and determined that we could make it to ZZZ at 10;000 feet; so we coordinated with Dispatch and informed them of the problem. We all decided to continue to ZZZ. The auto 1; auto 2 and manual modes of the pressurization system were working but the aircraft could not keep up with the pressurization at altitude. It appeared to be a valve stuck. However at a 10;000 feet and below there was no problem and we continued to ZZZ and landed on Runway XX uneventfully.
B757 Captain reported that a pressurization problem resulted in an expedited descent.