Question 983131
_________________rate____________time_____________distance
ToCity____________r______________(___)_____________260
ToHome___________r-5_____________(___)_____________260
TOTAL_____________________________12



_________________rate____________time_____________distance
ToCity____________r______________260/r_____________260
ToHome___________r-5_____________260/(r-5)_________260
TOTAL_____________________________12



{{{260/r+260/(r-5)=12}}}



{{{260(1/r+1/(r+5))=12}}}


{{{65(1/r+1/(r+5))=3}}}


{{{65(r+5+r)=3r(r+5)}}}


{{{3r^2+15r=65*2r+65*5}}}


{{{3r^2+15r=130r+325}}}


{{{3r^2-130r-325=0}}}------not  factorable; ...


{{{r=(130+- sqrt(130^2-4*3*(-325)))/(2*3)}}}


{{{r=(130+- sqrt(20800))/(2*3)}}}


{{{r=(130+- 10*sqrt(208))/(2*3)}}}


{{{r=(65+- 5*sqrt(208))/3}}}


{{{r=(65+- 20*sqrt(13))/3}}}, you must use the POSITIVE value.


{{{highlight(r=(65+20*sqrt(13))/3)}}}