DAY 434

PUZZLES FROM THE POLE VAULT
From a Polish puzzle magazine called Sam na Sam
Published in GAMES Magazine
August, 1986

When Adam reached the finish line of a 50-kilometer race, Eve was two kilometers behind him. The next day they decided to race again. To even up the contest, this time Adam started two kilometers behind Eve, while Eve began at the starting line as usual. Assuming they cycled at the same speeds as the day before, which cyclist won the second day's race - or was it a tie?

Answer:

Adam won again. Since Adam can cycle 50 kilometers in the time Eve can cycle 48, the two will be side by side 2 kilometers before the finish of their second race.  Since Adam is the faster cyclist, he will go on to win. 

His margin of victory, in case you're interested, will be
2 x (1 - 48/50) or .08 kilometers.