Casey Patterson of Topanga, Calif., was determined not to let a knee injury keep her from finishing a transcontinental crossing as it did last year. She stuck to a grueling year-long training regimen and brought chiropractors, masseuses and technicians on the Race Across America ultramarathon bicycle race.

The preparations paid off yesterday when Patterson, 43 and a mother of three, was the first woman to reach the finish at the Washington Monument, 11 days 21 hours 15 minutes 28 seconds after leaving San Francisco.

Cheryl Marek of Seattle, the only woman to challenge Patterson since the second day of the race, arrived at 7:41 last night and Marie Costellic of Mount Pleasant, Pa., the third and final competitor of the seven women starters, is expected to finish late this morning.

Of the 35 bicyclists to leave San Francisco last Saturday at 2 p.m., 19 finished. To be an official finisher, participants had to complete the race within 48 hours of the winner, Mike Secrest, who finished at 1:30 a.m. Tuesday. Robert Benorden, the 15th finisher in 11 days 10 hours 2 minutes, was the final man to finish officially. One rider will complete the race beyond the 48-hour period.