### Brain Teasers

# A Stooge Race

Moe, Larry, and Curly were trying to figure out who among them was the fastest, and by how much. They decide to settle this by a series of 2-man 100-meter races. In the first race, Moe beats Larry by exactly 10 meters. (That is to say, when Moe crosses the finish line, Larry is 10 meters behind him.) In the second race, Larry beats Curly by exactly 10 meters.

If they run at the exact same speeds as they did in their previous races (and their speed is constant over the entire course of the race), by what distance should Moe beat Curly when they race?

If they run at the exact same speeds as they did in their previous races (and their speed is constant over the entire course of the race), by what distance should Moe beat Curly when they race?

### Answer

19 meters.Instead of thinking about the distance one finishes ahead another, think of the total distance each racer covers. In the time it takes Moe to run 100 meters, Larry runs 90 meters, so his pace must be 90% of Moe's. In the time it takes Larry to run 100 meters, Curly runs 90 meters, so his pace is 90% of Larry's. Combining these two facts, we find that Curly's pace is 90% of (90% of Moe's), which is 81% of Moe's. So in the time that Moe runs 100 meters, Curly must run 81 meters, and therefore finish 19 meters behind Moe.

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