Question 169292: Please help with these two word problems. I just found out from the team leader that she did not post all of our assignments and these two are due tonight from me. I would greatly appreciate your help.
#94. Golden painting. An artist wants her painting to be in the
shape of a golden rectangle. If the length of the painting is
36 inches, then what should be the width? See the previous
exercise ***This is the previous exercise:Golden Rectangle. One principle used by the ancient Greeks to get shapes that are pleasing to the eye in art
and architecture was the Golden Rectangle. If a square
is removed from one end of a Golden Rectangle, as shown
in the figure, the sides of the remaining rectangle are
proportional to the original rectangle. So the length
and width of the original rectangle satisfy L/W=W/L-W.I hope this is understandable.
#84. Gone fishing. Debbie traveled by boat 5 miles upstream to
fish in her favorite spot. Because of the 4-mph current, it
took her 20 minutes longer to get there than to return. How
fast will her boat go in still water?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! "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)
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