+152 A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 5 hours and 20 minutes, but when there is a wind blowing from Penthaven to Jackson at 75 miles per hour, the trip takes 6 hours. How many miles is the distance from Penthaven to Jackson?
+128631 5 hrs 20 min = 5 + 1/3 hrs = (16/3)hrs
Call the rate of the plane in still air = R
With the wind the rate is R + 75
Against the wnid the rate is R - 75
Call the distance between the cities D
D/R = T
In the first instance
Total Distance / Rate in still air = 16/3 hrs
2D / R = (16/3)
D/R = 8/3
D = (8/3)R (1)
In the second instance
Time from Penthaven to Jackson + Time from Jackson to Penthaven = 6 hrs
D / ( R + 75 ) + D / ( R - 75) = 6 (2)
Sub (1) into (2)
(8/3)R / ( R + 75) + (8/3)R / ( R -75) = 6
(8/3)R ( R -75) + (8/3)R (R + 75) = 6 ( R+ 75)(R -75)
(8/3)R^2 - 200R + (8/3)R^2 + 200R = 6 ( R^2 - 5625)
(16/3)R^2 = 6R^2 - 33750
R^2 ( 6 -16/3) = 33750
(2/3)R^2 = 33750
R^2 = 50625
R= 225
The distance between the cities
D = (8/3)225 = 600 miles
+152 The problem says round trip, from Penthaven to Jackson and back. Then the problem says that the wind is blowing from Penthaven to Jackson during our round trip.
