At what rate is the bungee cord being stretched when the sideline runner reaches the 30 yard line?

Question

At halftime of a football game, two fan volunteers are attached together with a bungee cord and positioned on the sideline of the 50 yard line. One fan runs along the sideline at 4 yd/sec and the other runs on the 50 yard line towards midfield at 3 yd/sec. At what rate is the bungee cord being stretched when the sideline runner reaches the 30 yard line?

Answer 1

C = sqrt( A^2 + B^2) where A is the distance of the sideline and B is the distance of the 50 yard line

dC/dT = (1/2) * (2A dA/dt + 2B dB/dT) / sqrt( A^2 + B^2)

= (A dA/dt + B dB/dT) / sqrt( A^2 + B^2)

when A =20, then t=5 and B=15.

so the derivative is (20*4 + 15*3)/ sqrt( 20^2+15^2)

= (180+45)/ sqrt( 400+225)

= 225/sqrt(625)

= 225/25

= 9