Measure distance in astronomical units and time in years, so the constant in Kepler’s 3rd law is 1, i.e
P2=a3. The major axis of the ellipse is 2a=r1+r2 , so the semi-major axis is a=(r1+r2)/2 . Take r1=1 and r2=1.5 per the statement of the problem, then a=1.25 Then a3=P2=1.95 (rounded), so (approximately) P=1.4 . Since this is a one-way trip we divide by 2, getting a travel time of 0.7 years.
Nothing is required except Kepler’s laws and simple algebra and geometry. You do not even need Newton’s law of gravitation.
From Hilbert Space to Dilbert Space, and beyond 