Question 58071
Using: Distance (d) = ground speed/rate (r) * time (t).

We know the pilot goes West for d miles, then east for d miles.  The number of miles (d) in each direction is the same, because he returns to his starting point.

Therfore, lets break the problem into two pieces.
West:
d=?
r=450-5 (because the wind from the west will slow his ground speed)
t={{{t[w]}}}
Eq. 1 ==> {{{d=445*t[w]}}}

East:
d=d
r=450+5 (because the wind will increase his ground speed going the other way)
t={{{t[e]}}}
Eq.2 ==>{{{d=455*t[e]}}}

Finally, we know that the total time is three hours:
Eq. 3 ==> {{{t[e]+t[w]=3}}}

We have three equations and three unknowns.  Here's one way to solve them:
Eq 1 ==> {{{t[w]=d/445}}}
Eq 2 ==> {{{t[e]=d/455}}}
Plug those results into Eq. 3: {{{d/445 + d/455 = 3}}}
{{{d(1/445+1/455)=3}}}
{{{d=3/(1/445+1/455)}}}
{{{d=3/(0.004445)}}}
{{{highlight(d=674.9)}}} miles.