The 14th stage of the 2002 Tour de France was 221 km in length. The last 38 km i

Question

The 14th stage of the 2002 Tour de France was 221 km in length. The last 38 km is a tough, roughly steady, climb up Mount Ventoux and Lance and Richard are vying to win. When Lance has 6.0 km to go, he is told that the leader, Richard, is 4.0 minutes ahead of him and traveling at a constant speed. Lance speeds up to a rate 2.0 km/h faster than Richard to try and catch him. When Lance finishes, he learns that he has lost to Richard by 2.0 minutes. What was Lance's speed (km/h) over the last 6 km? Assume that both Richard and Lance stayed at a constant speed.

Explanation / Answer

let speed of rechard=Vr speed of lance=Vr+2 distance to cover for lance=6 distance to cover for richard=6-4*Vr 6/(2+Vr)=(6-4*Vr)/Vr +2 Vr=1.64 speed of lance=Vr+2=3.64

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