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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 $2$ 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?

 Dec 14, 2023
 #1
avatar+129185 
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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

 

cool cool cool

 Dec 15, 2023

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