OME 1967 Problem 3

A traffic light installed at a main junction of a road, in which you circulate in both directions, it remains red for $30$ s and green for another $30$ s, alternately. You want to install another traffic light on the same road, for a secondary crossing, located $400$ m away from the first, which works with the same period of $1$ min duration. It is wanted that the cars that circulate at $60$ km/h on the road in any of the two senses and that they do not have to stop if there was only the traffic light of the main intersection. They also don't have to stop after installing the secondary crossover. How many seconds can red be on at the secondary traffic light?

Note: It is suggested to reason on a Cartesian representation of the march of the cars, taking an axis of distances and another of times.