Question 226232
Let {{{s}}} = rate of airplane
Let {{{w}}} = rate of wind
{{{s + w}}} = rate flying with the wind
{{{s - w}}} = rate flying against the wind
given:
{{{t = 2.5}}} hrs with the wind
{{{t = 3.5}}} hrs against the wind
{{{d = 600}}} mi
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I can now write equations
{{{600 = (s + w)*2.5}}} 
{{{600 = (s - w)*3.5}}}
This is 2 equations and 2 unknowns, so it's solvable
{{{2.5s + 2.5w = 600}}}
{{{3.5s - 3.5w = 600}}}
Multiply both equations by {{{10}}}
{{{25s + 25w = 6000}}}
{{{35s - 35w = 6000}}}
Divide both equations by {{{5}}}
{{{5s + 5w = 1200}}}
{{{7s - 7w = 1200}}}
Multiply the 1st equation by {{{7}}} and
the 2nd equation by {{{5}}}
{{{35s + 35w = 8400}}}
{{{35s - 35w = 6000}}}
Add the equations
{{{70s = 14400}}}
{{{s = 205.71}}}
and, since
{{{5s + 5w = 1200}}}
{{{5*205.71 + 5w = 1200}}}
{{{5w = 1200 - 1028.57}}}
{{{5w = 171.429}}}
{{{w = 34.29}}} 
The wind speed is 34.29 mi/hr
check:
{{{600 = (s + w)*2.5}}}
{{{600 = (205.71 + 34.29)*2.5}}}
{{{600 = 239.996*2.5}}}
{{{600 = 599.989}}} close enough
and
{{{600 = (s - w)*3.5}}}
{{{600 = (205.71 - 34.29)*3.5}}}
{{{600 = 171.42*3.5}}}
{{{600 = 599.97}}} close enough