Question 1208722
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 $9$ hours. How many miles is the distance from Penthaven to Jackson?
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Let the ground speed of the plane when there is no wind = R mph
When the wind is a tail wind of 70 mph, the ground speed is R+70 mph
When the wind is a head wind of 70 mph, the ground speed is R-70 mph
Let T<sub>1</sub> = the time to go from P to J against a head wind.
Let T<sub>2</sub> = the time to go from J to P with a tail wind.

                          |distance|  rate  |  time  |
P to J to P (no wind)     |  2D    |   R    | 5 2/3  |
P to J (head wind)        |   D    | R-70   |   T<sub>1</sub>   |
J to P (tail wind)        |   D    | R+70   |   T<sub>2</sub>   |      

{{{system(DISTANCE=RATE*TIME, 2D=(R)(5&2/3),D=(R-70)*T[1],D=(R+70)*T[2],T[1]+T[2]=9)}}} 

Find a solver online for nonlinear systems. Perhaps
 
 https://www.wolframalpha.com/

Use t for T<sub>1</sub> and T for T<sub>2</sub>
since they don't usually take subscripted letters.

D≈325.89, R≈115.02, t≈1.7614, T≈7.2386

So the distance is approximately 326 miles.


Edwin</pre>