More than one way of skinning a cat but this is how I did it:-
Let distance from "speed change point" to destination be x
time (in mins) from start to "speed change point" t1 =
(300 - x)/260 (times by 60 to get minutes)
time (in mins) from "speed change point" to destination t2 =
(x/200) (times by 60 to get minutes)
Total time = 300/260 (x 60) + 8 = (900/13) + 8
Total time = t1 + t2
Therefore solve for:-
(900/13) + 8 = t1 + t2
Substitute for t1 and t2 and then resolve to get
x= 115.55555555 recurring!