A runs times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

200 m Explanation: Given: A runs times as fast as B A gives B a start of 80 m Concept used: Time = Distance/Speed Calculations: Let the speed of B be x So, speed of A = 5x/3 Let the total distance be 'a' m So, time taken by A to complete the total distance = a/(5x/3) = 3a/5x A gives B a start of 80 m Required distance for B = a - 80 Time taken by B to complete the distance = (a - 80)/x A and B might reach at same time &there4; Time taken by A to complete the total distance = Time taken by B to complete the distance ⇒ 3a/5x = (a - 80)/x ⇒ 3a = 5x - 400 ⇒ 2a = 400 ⇒ a = 200 &there4; The winning post must be 200 m far so that A and B might reach it at the same time

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