Let's use d as the variable name for the one-way distance. The flight's first phase consumed time #t_1# flying at 240 km/hr and time #t_2# flying at 320 km/hr. The total of those 2 time periods is
#t_"total" = t_1 + t_2 = 35 cancel("minutes")*((1 hr)/(60 cancel("minutes"))) = 0.583 hrs#
We need expressions for #t_1 and t_2#.
#t_1 = d/(240 "km"/"hr")" "# and #" "t_2 = d/(320 "km"/"hr")#
Going back to the equation for #t_"total"#, we will put in the above expressions for the 2 time periods.
#t_"total" = t_1 + t_2 = d/(240 "km"/"hr")" "+ " "d/(320 "km"/"hr")= 0.583 hrs#
Now, a bunch of algebra ...
#0.004167 "hr"/"km"*d" "+ " "0.003125 "hr"/"km"*d = 0.583 hrs#
#0.007292 "hr"/"km"*d = 0.583 hrs#
#d = (0.583 "hrs")/(0.007292 "hr"/"km") = 79.95 km#
I hope this helps,
Steve
