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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 $5$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $8$ hours.  How many miles is the distance from Penthaven to Jackson?

 
 Jan 1, 2024
 #1
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5 hrs 20 min  =   ( 5 + 1/3 ) hrs

 

Let the speed of the plane from Jackson to Penthaven =   S

 

Let the speed of the plane form Penthaven to Jackson  = S - 70

 

So

 

Rate * Time = Distance.......the dstance  between the towns is equal.....so....

 

S (5 + 1/3)  = (S - 70) (8)

 

5S + S/3  = 8S - 560

 

(16/3)S = 8S - 560

 

560 =  8S - (16/3)S

 

560  = (8/3)S

 

560 (3/8)  = S

 

210 =  S

 

Distance form Penthaven to Jackson =   (S -70) (8)  =  (210 - 70) (8)  =  1120 miles

 

cool cool cool

 Jan 2, 2024

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