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Algebra

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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 4 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 40 miles per hour, the trip takes 5 hours. 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.)

Mar 25, 2024

#1
+128794
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4 h 36 min =   4 + 36/60  =  4.6 hrs

Let the speed of the plane in still air = S

Let the speed of the plane against the wind = S  - 40

Let the speed of the plane with the wind = S + 40

Let the distance one way = D.... so round trip =  = 2D

Distance / Rate  =  Time

We have (with no wind)

2D / S  = 4.6

2D = 4.6S

D = 2.3S

With wind

D / (S + 40)  + D / (S -40)  = 5

D (S-40) + D (S + 40) = 5 (S + 40) (S - 40)

2DS  =  5 ( S^2  - 1600)

2 (2.3)S * S  =  5S^2  -  8000

4.6S^2  = 5S^2  - 8000

.4S^2  = 8000

S^2  =  (8000) / .4 =   80000/4  =  20000

S  =  sqrt (20000) =  141.42

D =  2.3 (141.42) ≈  325.3 miles

Mar 25, 2024