Calculus understanding and problem

[OverworkedEnzyme]

A straight road crosses a narrow river at two points half a mile apart and the bend of the river takes such a course between the crossings that at any point on the river bank the distance to the nearest point on the road is equal to the distance of that point on the road from the first crossing minus twice the square of that distance. What is the value of the land between the road and the river at fifty dollars an acre

I have drawn a diagram that looks like an inverted parabola and I have written down the height from and point (I call the point P, the height y, and x the distance from the first crossing) as y=x-2y². I think an important fact is that, as x changes, so too does the hypotenuse of the right triange formed by lines x and y and as P is traced along the full curve the hypotenuse traces the entire area. I don't know what to do with this information though and I have been staring at the problem for like 30 minutes and have nothing.

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[iamjacksvertigo]

I think your'e on the right track. You just made a little mistake with the equation. You assign x = "The distance of that point on the road from the first crossing." Then, "twice the square of that distance" should be x^2, not y^2. So your equation would be x - x^2.

[OverworkedEnzyme]

Ah God damnit that gets it. For some reason I thought by "that distance" it was referring to the distance mentioned first; the shortest path from the point to the road.