Let's assume that Kirby walks with a speed
[tex]v_1 = 3 mph[/tex]
for a time [tex]t_1[/tex], and that he runs with a speed
[tex]v_2 = 12 mph [/tex]
for a time [tex]t_2[/tex].
The total time available for Kirby to catch the train is:
[tex]t=56 min = 0.93 h[/tex]
and this must be equal to the sum of the two times t1 and t2:
[tex]0.93 = t_1 + t_2[/tex]
The distance Kirby should cover is
[tex]S=4 m[/tex]
and this should be equal to the sum of the distances covered by walking and by running:
[tex]4 = S_1 + S_2 = v_1 t_1 + v_2 t_2 = 3 t_1 + 12 t_2[/tex]
So we have a system of 2 equations:
[tex]0.93 = t_1 + t_2[/tex]
[tex]4 = 3 t_1 + 12 t_2[/tex]
If we solve the system, we find:
[tex]t_1 = 0.80 h = 48 min[/tex]
[tex]t_2 = 0.13 h = 8 min[/tex]
So, Kirby needs to run at least for 8 minutes in order to catch the train.
