CPM Homework Help : CALC Problem 10-30

After Barry hit a home run, Sammy leaves 1^st base for 2^nd traveling at $12$ feet per second. At the same time, Mark left 2^nd base for 3^rd traveling at $16$ feet per second. Assuming that the bases are $90$ feet apart, at what time after Barry hit the ball was the distance between Sammy and Mark at a minimum? What was the distance between them at that time?

Hint:

Sammy's distance is the horizontal leg of a right triangle. It is decreasing with time.
Write an expression for Sammy's distance (from second base).

Mark's distance is the vertical leg of a right triangle. It is increasing with time.
Write an expression for Mark's distance (from third base).

Use the Pythagorean Theorem to write an equation for the distance between Sammy and Mark.

Differentiate your equation and set it equal to $0$ to solve for the time when the distance between Sammy and Mark is a minimum.

Be sure to answer the question being asked.