Answer:
The time taken is [tex]t = 32.5 \ s[/tex]
Explanation:
From the question we are told that
The speed of first car is [tex]v_1 = 66.7 \ km/h = 18.3 \ m/s[/tex]
The speed of second car is [tex]v_2 = 52.7 \ km/h = 14.64 \ m/s[/tex]
The initial distance of separation is [tex]d = 119 \ m[/tex]
The distance covered by first car is mathematically represented as
[tex]d_t = d_i + d_f[/tex]
Here [tex]d_i[/tex] is the initial distance which is 0 m/s
and [tex]d_f[/tex] is the final distance covered which is evaluated as [tex]d_f = v_1 * t[/tex]
So
[tex]d_t = 0 \ m/s + (v_1 * t )[/tex]
[tex]d_t = 0 \ m/s + (18.3 * t )[/tex]
The distance covered by second car is mathematically represented as
[tex]d_t = d_i + d_f[/tex]
Here [tex]d_i[/tex] is the initial distance which is 119 m
and [tex]d_f[/tex] is the final distance covered which is evaluated as [tex]d_f = v_2* t[/tex]
[tex]d_t = 119 + 14.64 * t[/tex]
Given that the two car are now in the same position we have that
[tex]119 + 14.64 * t = 0 + (18.3 * t )[/tex]
[tex]t = 32.5 \ s[/tex]
