To solve this problem, let us say that:
v1 = the speed or velocity of Orson in travelling against the current
t1 = the time taken in travelling against the current
v2 = the speed or velocity of Orson in travelling with the current
t2 = the time taken in travelling with the current
It was stated in the problem that the time difference in travelling against the current and travelling with the current is 5 hrs, therefore:
t1 – t2 = 5
We know that:
t = d / v
Therefore:
(360 / v1) – (360 / v2) = 5
However we also know that:
v1 = v – 6
v2 = v + 6
where v is the velocity of the boat alone
[360 / (v – 6)] – [360 / (v + 6)] = 5
Multiplying everything by (v – 6) * (v + 6):
360 (v + 6) – 360 (v – 6) = 5 (v – 6) (v + 6)
360 v + 2160 – 360 v + 2160 = 5 v^2 – 180
4320 = 5 v^2 – 180
5 v^2 = 4500
v^2 = 900
v = 30
Therefore the speed of Orson’s boat is 30 miles per hour