Question 169292
"cross" multiplying __ L^2-LW=W^2 __ dividing by W^2 __ (L/W)^2-(L/W)=1


(L/W)^2-(L/W)-1=0 __ using quadratic formula __ (L/W)=[1ħsqrt(5)]/2


negative value is not realistic so L/W=[1+sqrt(5)]/2  __ this is the "Golden Ratio"


W=2L/(1+sqrt(5)) __ W=(2*36)/(1+sqrt(5)) __ W=22.25 (approx)



#84 __ working in miles and hours, so 20min is 1/3 hr __ t=d/r


let x="rate of boat" __ t=5/(x+4) __ t+(1/3)=5/(x-4)


substituting __ [5/(x+4)]+(1/3)=5/(x-4)


multiplying by 3(x+4)(x-4) __ 15x-60+x^2-16=15x+60


subtracting 15x+60 __ x^2-136=0 __ x=sqrt(136) __ x=11.66 (approx)