An airplane made a trip of 815 miles in 4 hours. part of the trip was made at 180 miles per hour and the remainder at 220 miles per hour. find the number of miles traveled at the slower rate.

We have 2 situation one with wind and one against wind

Speed = x , W= Wind

*case 1       ( With Wind)                     *case 2      ( Against Wind)

t=3 hr  d= 2160 m.  Rate = x + W            t=4 hr  d= 2160 m.  Rate = x - W

Distance = Rate * Time

2160 =  (x+W) * 3                                                      2160 = (x-W) * 4

2160 / 3 = (x+W)                                                        2160/4 = x-W

720 = x+W                                                                  540 = x-W

NOW 2 equations solve by substitution or elimination.  ( i did Elimination)

720 = x+W

540 = x-W

1260 = 2x    (W was eliminated) solve for x

x = 630  Speed of the Airplane 

now solve for W. W = 90  Speed of the Wind

 hope this helps

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