Question 258129
This is an RTD problem. Here is a table based on the given information:
PLANE . . . . .rate . . . . . . . . time . . . . . . . . . distance
with  . . . . . r+c = 600 . . . . . . Tw . . . . . . . . . . 600Tw
against . . . . r-c = 550 . . . . . . Ta . . . . . . . . . . 550Ta
total . . . . . . . . . . . . . . . . .5 . . . . . . . . . . 2900
we have two equations:
(i) {{{Tw + Ta = 5}}}
(ii) {{{600Tw + 550Ta = 2900}}}
we simplify (ii) to be 
(iii) {{{12Tw + 11Ta = 58}}}
multiply (i) by -11 to get
(iv) {{{-11Tw - 11Ta = -55}}}
adding (iii) and (iv) we get
{{{Tw = 3}}}
or 3 hours flying with the wind.
This means that 
{{{Ta = 2}}}
or 2 hours flying against the wind.