Mindbender

A: "We won the relay race," Tommy declared. "But not by much."

Uncle Fred smiled. "A win's a win, but what was the total difference?"

"Well, we had four in our team," the boy replied. "I ran a fifth of the distance, plus a fifth of a kilometre. Jim ran a quarter of the remaining distance, plus a quarter of a kilometre. Ted ran a third of the remaining distance, plus a third of a kilometre. Paul ran half the remaining distance, plus half a kilometre."

How far had Tommy run?