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A plane flies from Penthaven to Jackson and then back to Penthaven.  When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 20 miles per hour, the trip takes 4 hours and 45 minutes.  How many miles is the distance from Penthaven to Jackson?

(Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)

 Jun 4, 2023
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D ==distance

S ==Speed of the plane in still air.

 

2D ==3 + 36/60 ==3.6S..............................(1)

D/[S + 20] + D/[S - 20]==4.75.................(2), solve for D, S

 

Use substitution to get.

 

D==73.1645 miles - distance between Jackson and Penhaven.

 Jun 5, 2023

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