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Question Number 8757 by FilupSmith last updated on 26/Oct/16

A balloon is inflated such that every point expands at a units/second. An ant runs from one point A to another point B. If the ant moves b units/second, what will influence if or not the ant will ever reach point B?

$$\mathrm{A}\:\mathrm{balloon}\:\mathrm{is}\:\mathrm{inflated}\:\mathrm{such}\:\mathrm{that}\:\mathrm{every} \\ $$$$\mathrm{point}\:\mathrm{expands}\:\mathrm{at}\:{a}\:\mathrm{units}/\mathrm{second}. \\ $$$$ \\ $$$$\mathrm{An}\:\mathrm{ant}\:\mathrm{runs}\:\mathrm{from}\:\mathrm{one}\:\mathrm{point}\:\boldsymbol{{A}}\:\mathrm{to}\:\mathrm{another} \\ $$$$\mathrm{point}\:\boldsymbol{{B}}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{ant}\:\mathrm{moves}\:{b}\:\mathrm{units}/\mathrm{second}, \\ $$$$\mathrm{what}\:\mathrm{will}\:\mathrm{influence}\:\mathrm{if}\:\mathrm{or}\:\mathrm{not}\:\mathrm{the}\:\mathrm{ant}\:\mathrm{will} \\ $$$$\mathrm{ever}\:\mathrm{reach}\:\mathrm{point}\:\boldsymbol{{B}}? \\ $$

Commented by prakash jain last updated on 27/Oct/16

The shortest path between A and B does not change. The distance between A and B will also increase at a unit/sec. So the ant will reach B if b>a.

$$\mathrm{The}\:\mathrm{shortest}\:\mathrm{path}\:\mathrm{between}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{change}.\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{will}\:\mathrm{also}\:\mathrm{increase}\:\mathrm{at}\:{a}\:\mathrm{unit}/\mathrm{sec}. \\ $$$$\mathrm{So}\:\mathrm{the}\:\mathrm{ant}\:\mathrm{will}\:\mathrm{reach}\:\mathrm{B}\:\mathrm{if}\:{b}>{a}. \\ $$

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