Celestial Mechanics: Orbits 

How long would such a flight to Mars take?

From the figure, the major axis of the spacecraft’s orbit is 

1.5 AU + 1.0 AU = 2.5 AU

Therefore, the semimajor axis, a, is 1.25 AU

The period, P, of an orbit is given by

P² = a³
or
P² = 1.25³
So that
P = 1.4 years

This is the period of an object in a complete elliptical orbit, with semimajor axis 1.25 AU.  It will, therefore, take half of that time, or 0.7 years (about 8.5 months) for a spacecraft to reach Mars.