an aircraft flew 6 hours with the wind the return trip took

an aircraft flew 6 hours with the wind. the return trip took 7 hours against the wind if the speed of the plane in still air is 13 times the speed of the wind, find the wind speed and the speeed of the plane in an algebraic linear system.

Solution

D=RT
D=(13R+R)6=14R*6=84R
D=(13R-R)7=12R*7=84R
ANY DISTANCE THAT IS A MULTIPLE OF 84 MILES IS A SOLUTION.
PROOF:
LET THE RATE OF THE WIND=1 MPH.
D=84*1=84 MILES.
84=(13*1+1)*6
84=(13+1)*6
84=84
84=(13*1-1)*7
84=(13-1)*7
84=84
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LET THE RATE OF THE WIND=50 MPH.
84*50=(13*50+50)*6
4,200=(650+50)*6
4,200=700*6
4,200=4.200
4,200=(13*50-50)*7
4,200=(650-50)*7
4,200=600*7
4,200=4,200