The guiding principle of a crossing restriction is that the last ATC clearance has precedence over the previous clearance.
When the route or altitude is amended, the controller will restate altitude restriction.
"If altitude to maintain is changed or restated, whether prior to departure or while airborne, and previously issued altitude restrictions are omitted, those altitude restrictions are canceled."
Miles to descend to meet crossing restriction (3-degree descent) — altitude to lose (in thousands) times 3 plus 10 percent.
Three-degree rate of descent — halve the ground speed and add a zero.
Rate of descent — altitude to lose divided by time to fix.
To simplify for most jets — determine minutes from the fix (groundspeed divided by 60, or just glance over at the GPS or FMS); plan on descending at 2,000 fpm.
Your groundspeed at FL 310 is 420 knots, and you are cleared to cross 30 miles from the VOR at 10,000 feet and 250 kias. How far out would you need to start the descent?