### Brain Teasers

# An Unequal Race

Three friends planned to race each other on their bikes. Neil owned a good racing bike and had lots of experience (he belonged to a bike club), while Oscar had just learned to ride. The race seemed unfair, to say the least. After much discussion, they came up with a solution that seemed to allow a more equal race. They agreed on a distance of 50 miles and decided that the excellent biker, Neil, should form a team with the beginner, Oscar. They would bike against the other rider, Patrick, each riding half the distance and combining their time, while Patrick was to bike the full 50 miles by himself.

Who would win the race if Oscar could ride only half as fast as Patrick, while Neil rode four times as fast as Oscar?

Who would win the race if Oscar could ride only half as fast as Patrick, while Neil rode four times as fast as Oscar?

### Answer

If Oscar needs X minutes for the first half of the distance, Neil needs 1/4 times X minutes for the second half. Patrick consequently needs 1/2 times X minutes for half the distance and X minutes for the total.Oscar therefore takes exactly the same amount of time for the first half that Patrick takes for the entire distance, so Oscar and Neil lose the race.

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