A train heads strait east at constant speed at 9 am At noon

A train heads strait east at constant speed at 9 am. At noon, a car heads strait east at twice the speed of the train. What time will it be when the car catches up to the train?

Solution

d = rt
.
Let x = speed of train
then
2x = speed of car
.
Let t = hours train was traveling
.
xt = (2x)(t-3)
xt = 2xt-6x
0 = 2xt-6x-xt
0 = xt-6x
0 = x(t-6)
0 = t-6
6 hours = t
.
Car catches up with train at 3 pm.