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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? (Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)

Apr 20, 2022

#2
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Let the distance netween Penthaven and Jackson==D

Let the speed of the plane with no wind==S

The speed of the plane against the wind ==S - 50

S * [6 + 24/60] ==D.....................(1)

[S - 50] * [6 + 40/60]==D............(2), solve for S, D

S==1,250 mph - speed of the plane with no wind.

D==8,000 miles - distance between Penthaven and Jackson.

Apr 20, 2022
#3
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Note: The distance D==4,000 miles NOT 8,000. It wouldn't let me EDIT the answer!

Guest Apr 20, 2022
#4
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Let the distance between Penthaven and Jackson==D
Let the speed of the plane with no wind==S
The speed of the plane against the wind==S - 50
The speed of the plane with the wind==S + 50

S * [6 + 24/60] ==2D,
D / [S + 50] + D / [S - 50]==6 + 40/60, solve for S, D

S==250 mph - speed of the plane with no wind
D==800 miles - distance between Penthaven and Jackson

Apr 20, 2022
#5
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