+60 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 30 miles per hour, the trip takes 3 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.)
+130104 3 hrs 36 min = 3.6 hrs
3 hrs 45 min = 3.75 hrs
Speed of plane = P
Speed of Wind = 30
Distance between cities = D
Distance / Rate = Total Time .....so...
With no wind.....
2D / P = 3.6
D / P = 1.8
D = 1.8 P
With wind....
D / ( P + 30) + D / (P -30) = 3.75
1.8P ( P -30) + 1.8P ( P + 30) = 3.75 ( P -30) (P+ 30)
3.6P^2 = 3.75 (P^2 - 900)
.15P^2 = 3375
P^2 = 3375/.15
P^2 = 22500
P = 150
D = 1.8 ( 150) = 270 miles
