KöMaL 2010 K240

A company of $T$ members went on a trip to the countryside. Exactly half of them went on foot. The distance to the destination was $T$ kilometres along the footpath, and they covered it in 1 hour. The other half of the company went by bike along another route. Their speed (not counting periods when they stopped) was $T$ less than $T$ times the speed of the walkers. The bikers had to stop on their way for $T$ minutes because of a flat tire, and later on they had to stop again, for $T$ times as much time, because of a broken chain on another bike. When they continued the journey, a biker with no technical problems so far took the lead of the group for $T$ minutesminutes, and then let somebody else to take the lead. Finally, the bikers arrived at the destination $T$ minutes sooner than the walkers. How long was the footpath, and how long was the bike route?