Question:

A runs \( 1 \frac{2}{3} \) times as fast as B. If A gives B a start of 80m, how far must the winning post be, so that A and B might reach it at the same time?

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Use relative speed concepts carefully in problems where one runner gives a head start to another.
Updated On: Mar 7, 2025
  • 200 m
  • 300 m
  • 270 m
  • 160 m
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The Correct Option is A

Solution and Explanation

Let B’s speed be \( x \), then A’s speed is: \[ \frac{5}{3} x \] Let the total race distance be \( d \), and B runs \( d - 80 \) meters.
Since both finish at the same time: \[ \frac{d}{\frac{5}{3}x} = \frac{d - 80}{x} \] Cross multiplying: \[ 3d = 5(d - 80) \] \[ 3d = 5d - 400 \] \[ 2d = 400 \] \[ d = 200 \] Thus, the winning post must be 200 meters.
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