5 mph
The relationship between distance, speed, and time is ...
... time = distance / speed
If we let g represent the speed of the Gulf Stream current (in mph), the speed of the ship with the current is 31+g, and the speed against the current is 31-g.
The times for the two distances are equal, so we can write ...
... 288/(31+g) = 208/(31-g)
Multiplying by the product of the denominators gives ...
... 288(31 -g) = 208(31 +g)
... 31(288 -208) = g(208 +288) . . . . . add (288g - 208·31)
... g = 2480/496 = 5 . . . . . . . . . . . . . divide by the coefficient of g
The rate of the Gulf Stream is 5 mph.
