Question

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.

Answer 1

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

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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