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?

Lilliam0216 Mar 2, 2024

#1**+1 **

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

CPhill Mar 2, 2024

#2**0 **

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.

Lilliam0216
Mar 2, 2024