Quarrie made the Jamaican 100 m team for the 1968 Summer Olympics as a 17-year-old, but he injured himself in training, and could not take part. He moved to the United States and attended the University of Nebraska and later the University of Southern California, where he graduated with a degree in Business and Public Administration. There, his sprinting capabilities gradually increased. At the 1970 Commonwealth Games, Quarrie won the gold medal in both the 100 and 200 m, surprising his more experienced competitors. Anchoring the Jamaican 4 × 100 m relay team, he pocketed a third Commonwealth title. Quarrie repeated his sprint double the following year at the Pan American Games in Cali and his time in the 200 meters was a hand-timed 19.8. One of the favourites for the upcoming Munich Olympics, Quarrie again suffered from injuries at the Olympic Games. He did compete in the 200 m but had to abandon his 200 m semi-final after pulling a muscle. In 1974 Quarrie repeated his 1970 performance by grabbing the 100 and 200 m titles at the Commonwealth Games in Christchurch, becoming the first athlete to retain the title in either event. The next season, he again tied the 200 m world record, 19.8. He also tied the 100 m record with a hand-timed mark in 1976 at the California Relays at Modesto Junior College, one of only a few athletes to have held these records simultaneously. This time was actually 10.07 seconds. In 1976 after winning the AAA's 100/200 titles Quarrie could finally compete at the Olympics without injuries. He first made the 100 m final, which he led until overtaken by Trinidadian Hasely Crawford. In the 200 m Quarrie led the pack coming out of the turn and held off all challenges to take the title in 20.22. At the 1978 Commonwealth Games he won his third consecutive 100 m title but was eliminated in the 200 m after a cramp attack. Quarrie's participation in his fourth Olympics in Moscow was in doubt after he was involved in a car crash the previous year. He recovered in time to compete but was eliminated in the 100 m semi-finals. His title defense failed in the 200 m but he did make the final and finished third, adding a bronze medal to his collection. By 1984 Quarrie was no longer among the world's best in the individual sprint events and it was therefore no surprise he was eliminated in the heats of the 200 m event at the Los Angeles Olympics. However, he won a fourth Olympic medal with the Jamaican relay team, which finished second behind the United States. His final competitive race was a 200m in London in September 1984, in which he finished 3rd.
