Question 130733
{{{r[a]}}}, air speed
{{{r[w]}}}, wind speed


Then ground speed with a head wind is {{{r[a]-r[w]}}} and ground speed with a tail wind is {{{r[a]+r[w]}}}


To travel 1000 miles in 4 hours, ground speed must be {{{1000/4=250}}} mph.


To travel 1000 miles in 3 hours 20 minutes, which is 3 and 1/3 hours, or 10/3 hours, ground speed must be {{{1000/(10/3)=300}}} mph.


So:

{{{r[a]-r[w]=250}}}, and
{{{r[a]+r[w]=300}}}


Add the two equations, term by term:
{{{2r[a]+0r[w]=550}}}


Divide by 2:
{{{r[a]=275}}}


Since {{{r[a]-r[w]=250}}} and {{{r[a]=275}}},


{{{275-r[w]=250}}}
{{{r[w]=25}}}


So the air speed is 275, and the wind speed is 25.