I am not sure that this will help you but I did this a different way and got your answers.
cycle: rate = (x+30)km/hr; t = .26 hours
run: rate = x km/hr; t = .8 hours
using d = rt
d = .26(x + 30)
60 - d = .8x
60 - .26x - 7.8 = .8x
52.2 = 1.06x
x = 49.24...its about the same with rounding error. I've looked and I've looked but I can't see the error. Sorry.