+84 A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours and $50$ 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.)
+130462 3 hrs 20 min = 3 + 1/3 hrs = 10/3 hrs
3 hrs 50 min = 3 + 5/6 hrs = 23/6 hrs
Total time = 43/6 hrs
Let the distance between the towns = D
Let the speed of the plane with no wind = S
Let the speed of the plane against the wind = S - 70
Distance / Rate = Time
With no wind
D / S = 10/3
D = (10 / 3) S
With wind against the plane
D / (S -70) = 23/6
(10/3)S = (23/6) (S -70)
(10/3)S = (23/6)S - 1610 / 6
(23/6 - 10/3)S = 805 / 3
(23/6 - 20/6)S = 805/3
(3/6)S = 805/3
(1/2)S = 805/3
S = 1610 / 3
Distance = Rate * Time = (1610/3)(10/3) ≈ 1788.9 miles
