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.)
Let the distance between Penthaven and Jackson be d miles. Let the speed of the plane in still air be s miles per hour.
When there is no wind, the plane flies from Penthaven to Jackson at speed s and then back at the same speed. The total time for the round trip is 2d/s hours.
When there is wind, the plane flies from Penthaven to Jackson at speed s+30 miles per hour and then back at speed s−30 miles per hour. The total time for the round trip is 2d/(s+30)+2d/(s−30) hours.
We are given that the round trip time with no wind is 3 hours and 36 minutes, or 198/60 hours, and the round trip time with wind is 3 hours and 45 minutes, or 210/60 hours. Setting these two equations equal to each other, we get:
s2d=60198ands+302d+s−302d=60210.
Solving these equations, we find that s=250 miles per hour and d=800 miles.
Therefore, the distance between Penthaven and Jackson is 800 miles.
