A car and a truck leave the same place at the same time. The car drives North at 60 miles per hour and the truck drives west at 45 miles per hour. How fast is the distance changing between the car and the truck after 2 hours?

Drawing a diagram gives:
$LaTeX: \displaystyle c$ can be found using the Pythagorean theorem $LaTeX: \displaystyle c=\sqrt{(120)^2+(90)^2}=150$ . Using the Pythagoren Theorem and implicit differentiation gives $LaTeX: \displaystyle c^2=a^2+b^2 \iff 2c\frac{dc}{dt}=2a\frac{da}{dt}+2b\frac{db}{dt}$ . Solving for the unknown rate gives $LaTeX: \displaystyle \frac{dc}{dt}=\frac{a}{c}\frac{da}{dt}+\frac{b}{c}\frac{db}{dt}$ .Evaluating gives $LaTeX: \displaystyle \frac{dc}{dt}=75$