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-eve

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

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

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

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

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