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?

bingboy Dec 14, 2023

#1**+1 **

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

CPhill Dec 15, 2023