Three Runners, One Winner
Algebra
Level
2
Rooney, Hernandez, and Robin race each other in a 100 meter race. All of them run at a constant speed throughout the race.
If Rooney beats Hernandez by 20 meters and Hernandez beats Robin by 20 meters, then by how many meters does Rooney beat Robin?
The answer is 36.
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Rooney ran 100m in the time that it took Hernandez to run 80. So, Rooney's speed is 4 5 of Hernandez's. Hernandez ran 100m in the time that it took Robin to run 80. So, Hernandez's speed is 4 5 of Robin's. Rooney's speed is 4 5 * 4 5 = 1 6 2 5 of Robin's speed. Multiply the numerator and denominator of the fraction by 4, and you get 6 4 1 0 0 , meaning that Rooney ran 100m(finishing the race) in the time that it took Robin to run 64, beating him by 100-64 = 36 meters.