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# Jane is 2 mi offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat She can row 2 mph and can walk 4 mph Where should she land her?

r = distance she rowed
w = distance she walked
t = total time to reach village

t = r/2 + w/5

r^2 = 2^2 + (6 - w)^2
r = (4 + 36 - 12w + w^2)^(1/2)
r = (w^2 - 12w + 40)^(1/2)

t = (w^2 - 12w + 40)^(1/2)/2 + w/5
t' = (1/2)(1/2)(w^2 - 12w + 40)^(-1/2)(2w - 12) + 1/5 = 0

(1/2)(1/2)(w^2 - 12w + 40)^(-1/2)(2w - 12) = -1/5
(1/2)(w - 6) = -1/5(w^2 - 12w + 40)^(1/2)
5(w - 6) = -2(w^2 - 12w + 40)^(1/2)
25(w^2 - 12w + 36) = 4(w^2 - 12w + 40)
(25 - 4)w^2 + (-25*12 + 4*12)w + 25*36 - 4*40 = 0
21w^2 - 252w + 740 = 0
w = 6.87, 5.13 mi

r = (w^2 - 12w + 40)^(1/2)
r = 2.18 mi

She should land her boat 5.13 miles away from village Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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