I get $$0.36 \times x + 0.72 \times \sqrt{2500+(100-x)^2}$$ for $$x = 100 - \frac{50}{\sqrt{3}} \approx 71.132487$$ is [$$\approx 67.1769s$$](https://www.wolframalpha.com/input?i2d=true&i=0.72*Sqrt%5B2500%2BPower%5B%5C%2840%29100-x%5C%2841%29%2C2%5D%5D%2B+0.36*x%5C%2844%29+x%3D100-Divide%5B50%2CSqrt%5B3%5D%5D).


I wonder why our answers are off by 0.04


south_korea_ln

science

[Math puzzle] Fastest route from A to B

Scroogey

I think the answer is to walk horizontally along the edge of the rectangle for 71.13m, then walk in a straight line to point B.

Letting $$w = 100$$m (the horizontal distance from A to B) and let $$h = 50$$m (the vertical distance). Let $$x$$ be the number of meters to walk horizontally before going in a straight line.  The total time is:

$$ 
\frac{x}{10\text{km/h}} + \frac{\sqrt{(w-x)^2 + h^2}}{5\text{km/h}}
$$

You can use calculus to find the optimal value of $$x = w - h/\sqrt{3}$$