+1791 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.)
+128475 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
