Rate of Change for distance

[volleyball11]

Could somebody please help me solving this problem?

Train A is heading south from Milwaukee at a rate of 50 miles per hour. Train B is heading west from Milwaukee at a rate of 72 miles per hour. If they both leave at 12 noon, what is the rate of change for the distance between the trains when it is 4pm?

 

[stapel]

Draw the right triangle, with "Milwaukee" at the origin, so A is going down the y-axis and B is heading left on the x-axis.

Figure out their distances x and y from the origin after four hours. (Ignore signs; just find the absolute distances.) Use the Pythagorean Theorem to find their distance D from each other.

Note that, disregarding direction, dy/dt = 50 and dx/dt = 72.

Use the Pythagorean Theorem to construct the distance equation. Differentiate implicitly, plug in the known values for x, y, D, dy/dt, and dx/dt. Solve for dD/dt.

Eliz.