Calculus question

Question

Two people walk away from the same location at the same time. The first person travels east at a rate of 2.5 m/s. The second person travels south at a rate of 1.5 m/s. At what rate is the distance between them increasing 5 minutes later?

Answer 1

D = sqrt( x^2 + y^2) where x is the eastboad walker and y is the southbound walker

Implicit differentitation:

dD/dt = 1/2* (2x dx/dt + 2y dy/dt) / sqrt( x^2 + y^2)

(x dx/dt + y dy/dt) / sqrt( x^2 + y^2) <--- first derivative

In 5 minutes, the eastbound walker has traveled x=5*2.5 = 12.5
and the southbound walker has traveled y=5 * 1.5 = 7.5

dx/dt = 2.5 and dy/dt = 1.5

dD/dt = (12.5*2.5 + 7.5*1.5) / sqrt( 12.5^2 + 7.5^2)

= 42.5/ sqrt(212.5)

=2.9154759474225....