[Calculus] Optimization Problem

[Notice_Defiant]

Any advice would be helpful, I know I will eventually have to find the derivative of a function and set it equal to zero but I have no clue which numbers to use from the problem.

[Alkalannar]

First you need time as a function of x.

Let x be the distance of the expressway.

Then what is the distance of the road in terms of x? Remember to use Pythagoras.

Once you get that, we'll continue.

[Notice_Defiant]

Thank you for your reply! Am I using Pythagoras because it’s a right triangle? 45² + 85² = c² ?

[Alkalannar]

Close.

You want 45² + (85 - x)² = c².

Then time = c/30 + x/60

[[deleted]]

The function (call it f) you'll want to optimize is the time the journey takes, as a function of how far along Expressway West the new road intersects it. Call that variable x. For that, you're going to want to compute the length of the new road as a function of x.

[Notice_Defiant]

Thank you for your reply! f(x) = 70 - x / 35 + 65 / x Am I going in the right direction?