After time t seconds, the first car is 165-25t feet away from the sign and the other car is 110-35t feet from the sign. The two cars and the sign form a right triangle with legs equal to the aforementioned distances.
The hypotenuse of the triangle has length x=√((165-25t)²+(110-35t)²).
dx/dt=(-15950+3700t)/√(39325-15950t+1850t²) is the rate of change of the straight line distance between them.
When t=1, dx/dt=-12250/√25225=-12250/158.8238=-77.13 ft/s approx. The negative sign indicates a decreasing rate of change (speed).