time = distance/speed
total time = time for part 1 + time for part 2 + time for part 3
.. t = 5/r +6/(0.6r) +1/(r+1)
.. = (1/r)*(5 +6/0.6) +1/(r +1)
.. = 15/r +1/(r +1)
Add these fractions in the usual way.
.. = (15(r +1) +r)/(r(r +1))
.. t = (16r +15)/(r(r +1)) . . . . . . . . . your expression for t
For r=3, this is
.. t = (16*3 +15)/(3*(3 +1))
.. = 63/12
.. = 5 3/12
.. = 5 15/60
The trip takes 5 hours and 15 minutes