A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $6$ hours and $24$ minutes, but when there is a wind blowing from Penthaven to Jackson at $50$ miles per hour, the trip takes $6$ hours and $40$ minutes. How many miles is the distance from Penthaven to Jackson

Answer: Given : A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 6 hr 24 mins , but when wind is at 50 miles per hr than 6 hrs 40 mins.

To find : distance from Penthaven to Jackson

Solution:

Let say Plane speed when no Wind = P Miles/hr

& Distance between Penthaven to Jackson = D Miles

Time taken in round trip = D/P + D/P

= 2D/P

6 hr 24 mins = 6 hr + 24/60 hr = 6.4 hrs

=> 2D/P = 6.4

=> D/P = 3.2

=> P = D/3.2

when there is a wind blowing from Penthaven to Jackson at $50$ miles per hour,

=> Time taken = D/(P + 50) + D/(P - 50)

Time taken = 6 hr 40 mins = 6 hr + 40/60 hr = 6 + 2/3 = 20/3 hrs

=> D/(P + 50) + D/(P - 50) = 20/3

=> 3D(P - 50+ P + 50) = 20(P² - 2500)

=> 3D ( 2P ) = 20(P² - 2500)

=> 3D P = 10 (P² - 2500)

=> 3D (D/3.2) = 10 ( (D/3.2)² - 2500)

=> 3D² * 3.2 = 10 ( D² - 25600)

=> 9.6D² = 10D² - 256000

=> 0.4D² = 256000

=> D² = 6,40,000

=> D = 800

distance from Penthaven to Jackson = 800 Miles

Additional info :

Plane speed = 800/3.2 = 250 miles per hr

Step-by-step explanation:

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