Question 246029
Determine how far each car has travelled in 3 hours using 
Distance = rate x time 
Car A = 60mph x 3 hrs = 180 miles
Car B = 35 mph x 3 hrs = 105 miles

Draw a right triangle 
Label the horizontal leg "x = 180"
Label the vertical leg "y = 105"
Label the hypotenuse "z"

Using the Pythagorean Theorem, solve for z:
{{{x^2 + y^2 = z^2}}}
{{{180^2 + 105^2 = z^2}}}
{{{32400 + 11025 = z^2}}}
{{{43425 = z^2}}}
{{{z = 208.39}}}

Before you proceed with the calculus identify your variables:
Distances
Let x = 180
Let y = 105
Let z = 208.39
Rates of change
Let dx/dt = 60 
Let dy/dt = 35
The variable you are solving for is dz/dt, the rate of change (i.e. how fast the two cars are moving apart after 3 hours)

Differentiate the Pythagorean Theorem:
{{{x^2 + y^2 = z^2}}}
{{{(2x)(dx/dt) + (2y)(dy/dt) = (2z)(dz/dt)}}}
Simplify the equation by dividing each term by 2
{{{(x)(dx/dt) + (y)(dy/dt) = (z)(dz/dt)}}}

Substitute the values from above
{{{(180)(60) + (105)(35) = (208.39)(dz/dt)}}}
Solve for dz/dt:
{{{10800 + 3675 = 208.39 (dz/dt)}}}
{{{14475 = 208.39 (dz/dt)}}}
Dividing both sides by 208.39:
{{{dz/dt = 69.46mph}}}
This is how fast the two cars are moving away from each other.