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An ant travels from point A(0, -63) to point B(0, 74) as follows. It first crawls straight to (x, 0) with \(x \ge 0\), moving at a constant speed of sqrt2 units per second. It is then instantly teleported to the point (x, x). Finally, it heads directly to B at 2 units per second. What value of x should the ant choose to minimize the time it takes to travel from A to B?

Thank you very much!

:P

CoolStuffYT Feb 25, 2019

#1**+2 **

Here's my best attempt

Time = [distance from (0, -63) to (x , 0)] / rate plus [ distance from (x, x) to (0, 74) ] / rate

Time = √ (x^2 + 63^2) / √ 2 + √ [x^2 + (74 - x)^2 ] / 2

We could use Calculus to solve this, but a graph seems easier

Here is a graph of the function : https://www.desmos.com/calculator/mmudrsppbh

It shows that the time is minimized when x ≈ 23.3

And the minimized time ≈ 75.4 sec

CPhill Feb 25, 2019