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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 8, 2023
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D==Distance from Jackson to Penthaven

S ==Speed of the plane in still air.

 

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

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

 

D==73.1645 miles - one-way distance from Jackson to Penthaven.

 Jun 8, 2023

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