In a relay race, the first runner of the team runs one-half of the distance plus one-half of a kilometre; and the second runner reached the finish line after running one-third of the remaining distance plus one-third of a kilometre. How long was the race?

Question

In a relay race, the first runner of the team runs one-half of the distance plus one-half of a kilometre; and the second runner reached the finish line after running one-third of the remaining distance plus one-third of a kilometre.  How long was the race?

anonymous · Answer

5 km
check:
(5/2+1/2) + (5/3+1/3) = 5

anonymous · Answer

let D = distance of the race.
runner 1 ran D/2 + 1/2 
runner 2 ran D/3 + 1/3
total distance = runner1 + runner2
D = (D/2+1/2) + (D/3+1/3)
solving for D gives 5.