A problem by Lakkoju Dilip
Level
pending
Rooney, Hernandez, and Robin race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Rooney beats Hernandez by 20 meters. Hernandez beats Robin by 20 meters.
How many meters does Rooney beat Robin by ?
The answer is 36.
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I think the best way ( not the shortest) to approach this question is first of all find the relative distances for each runner when the first runner crosses the finish line at time t. From the [Distance/Speed= Time] equality, we know that 100/Vrooney=80/Vhernandez and 100/Vhernandez=80/Vrobin Therefore, Vrooney/Vhernandez= 5/4 and likewise, Vhernandez/Vrobin=5/4 So, now lets find the ratio of their relative speed to one another: In other words, we want to know Vrooney:Vhernandez:Vrobin which comes out to 5:4:3.2. ( Note: 5/4=4/3.2) Last step, we want to know the distance of each runner has traveled relative to Rooney when Rooney crosses the finish line at time t: t= 100/5: 80/4:x/3.2 where t is the time it took Rooney to complete 100m.
=> 20= x/3.2 and x= 20 * 3.2= 64 meter. Hence, Rooney beat Robin by 10-64=36