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.)

tomtom Mar 25, 2024

#1**+1 **

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

CPhill Mar 25, 2024