The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 4 cm/s. when the length is 11 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

This is a nice "rates of change" problem from Calculus.

Let the length and width of the rect. be L and W.  We are given the following info:

dL/dt = 6 cm/s; dW/dt = 4 cm/s; L = 11 cm and W = 5 cm.

The area of the rect. is A = L*W.  Differentiating, 

dA/dt = L(dW/dt) + W(dL/dt).

Subst. the given info:  dA/dt = (11 cm)(4 cm/sec) + (5 cm)(6 cm/sec).

Just evaluate this to find dA/dt:  (44 + 30) cm^2/sec = 76 cm^2/sec 

Using the rise/run rule. you would get 2/6.simp. 1/3