Question

Kirby is four miles from the train station, from which a train is due to leave in 56 minutes. Kirby is walking along at 3 mph, and could run at 12 mph if it were necessary. If Kirby wants to be on that train, it will be necessary to do some running! How many miles of running?

Answer 1

Let's assume that Kirby walks with a speed 
$v_1 = 3 mph$
for a time $t_1$, and that he runs with a speed
$v_2 = 12 mph$
for a time $t_2$.

The total time available for Kirby to catch the train is:
$t=56 min = 0.93 h$
and this must be equal to the sum of the two times t1 and t2:
$0.93 = t_1 + t_2$ 

The distance Kirby should cover is
$S=4 m$
and this should be equal to the sum of the distances covered by walking and by running:
$4 = S_1 + S_2 = v_1 t_1 + v_2 t_2 = 3 t_1 + 12 t_2$

So we have a system of 2 equations:
$0.93 = t_1 + t_2$
$4 = 3 t_1 + 12 t_2$

If we solve the system, we find:
$t_1 = 0.80 h = 48 min$
$t_2 = 0.13 h = 8 min$

So, Kirby needs to run at least for 8 minutes in order to catch the train.