## Problem of the Day #302: Optimal Path
*January 15, 2012*

*Posted by Albert in : potd , trackback*

Alex is trying to run to Saketh as fast as he can in Coordinatesville. Alex starts off at $(0 \text{m}, 0 \text{m})$ and runs to Saketh at $(10 \text{m} , 10 \text{m})$. Given that Coordinatesville gets increasingly muddy for increasing $x$, such that Alex’s speed $v$ (in meters per second) is given by $v(x) = e^{x^2} \frac{\text{m}}{\text{s}}$, find the minimum amount of time it takes for Alex to reach Saketh.

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