Without any wind an airplane flies at 200 miles per hour. the plane travels 800 miles into the wind and then returns with the wind in in a total time of 8 hours and 20 mins. find the average speed of the wind.

800 = ( 200 - s ) × t1 ;
800 = ( 200 + s ) × t2 ;
t1 + t2 = 8h 20 mins.;
where s = the average speed of the wind ;
t1 = the time into the wind ;
t2 = the time with the wind ;
Then, t1 = 800 / ( 200 - s ) and t2 = 800 / ( 200 + s ) ;
800 / ( 200 - s ) + 800 / ( 200 + s ) = 8h and 20 mins. = 500 mins. ;
8 / ( 200 - s ) + 8 / ( 200 + s ) = 5 ;
8( 200 + s ) + 8( 200 - s ) = 5( 200 + s )( 200 - s ) ;
1600 + 8s + 1600 - 8s = 5( 4000 - s^2 ) ;
3200 = 20000 - 5s^2 ;
5s^2 = 17800 ;
s^2 = 17800 ÷ 5 ;
s^2 = 3560 ;
s = ≈ 60 miles per hour ;