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A plane flies from Springville to Brockton and then back to Springville. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Springville to Brockton at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Springville to Brockton?
 

 Mar 15, 2020
 #1
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rate * time = distance

 

distance to and from is the same

 

r * 6.4   = 2d        or      r * 3.2 = d

d/(r-50) + d /(r+50) = 6.667         (I changed the minutes to hours)

 

3.2r /(r-50)  + 3.2r (r+50) = 6.667

3.2r (r+50) + 3.2r ( r-50) = 6.667 ( r+50)(r-50)

3.2 r^2  + 160r   + 3.2r^2  - 160r  =  6.667 r^2 -16667.5

-.2667 r^2 + 16667.5 = 0                   quadratic formula shows x = 250 m/hr

 

250 m/hr x 6.4 hrs = roundtrip distance = 1600 miles       800 miles one way

 Mar 15, 2020

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