+743 A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $2$ hours and $40$ minutes, but when there is a wind blowing from Penthaven to Jackson at $50$ miles per hour, the trip takes $3$ hours and $30$ minutes. How many miles is the distance from Penthaven to Jackson?
+129849 2 hrs 40 min = 2 + 2/3 hrs = 7/3 hrs
3 hrs 30min = 3 + 1/2 hrs = 7/2 hrs
Distance = Rate * Time
Let the speed of the plane in still air = S
When there is no wind it is traveling (S) mph and against the wind it is traveling (S - 50) mph
So.....equating the same distance
S * ( 7/3) = (S - 50) ( 7/2)
(7/3)S = (7/2)S - 175
175 = ( 7/2 - 7/3)S
175 = (7/6)S
S = 175 ( 6/7) = 150 mph in still air
So....the distance between cities is (150) (7/3) = 350 miles
