Answer:
70 mph
Explanation:
We can write the position of the car at time t as
[tex]x_c (t) = v_c t[/tex]
where [tex]v_c[/tex] is the speed of the car, while the position of the truck is
[tex]x_t (t) = d + v_t t[/tex]
where
[tex]d = 30 mi[/tex] is the initial distance between the car and the truck (at 3:00 pm)
[tex]v_t = 50 mph[/tex] is the speed of the truck
The car overcomes the truck when they have same position, so
[tex]x_c = x_t\\v_c t = d + v_t t[/tex]
This occurs at 4:30 pm, so 1:30 h (1.5 h) after the initial instant. So, by using
t = 1.5 h
And solving the equation for [tex]v_c[/tex], we find the speed of the car:
[tex]v_c =\frac{d}{t}+v_t=\frac{30}{1.5}+50=70 mph[/tex]
