SOLUTION: You are in a boat a miles from the nearest point on the coast (see figure). You are to go to a point Q, which is b miles down the coast and 1 mile inland. You can row at 4 miles pe

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Question 593418: You are in a boat a miles from the nearest point on the coast (see figure). You are to go to a point Q, which is b miles down the coast and 1 mile inland. You can row at 4 miles per hour and walk at 5 miles per hour. If a = 2, and b = 4, toward what point on the coast should you row in order to reach Q in the least time? (Round your answer to three decimal places.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite the problem:
You are in a boat 2 miles from the nearest point on the coast (see figure, it would be nice!).
You are to go to a point Q, which is 4 miles down the coast and 1 mile inland.
You can row at 4 miles per hour and walk at 5 miles per hour.
Toward what point on the coast should you row in order to reach Q in the least time?
:
Let x = distance from the coastal point nearest the boat, to where he should land the boat
then
(4-x) = distance from the landing point to the coastal point nearest Q
:
The distance rowed and and walked will be the hypotenuse of two triangles
write a time equation; time = dist/speed
:
total time = rowing time + walking time
t(x) = %28sqrt%282%5E2%2Bx%5E2%29%29%2F4 + %28sqrt%281%5E2%2B%284-x%29%5E2%29%29%2F5
:
t(x) = %28sqrt%284%2Bx%5E2%29%29%2F4 + %28sqrt%281%2B%2816-8x%2Bx%5E2%29%29%29%2F5
:
t(x) = %28sqrt%284%2Bx%5E2%29%29%2F4 + %28sqrt%28x%5E2-8x%2B17%29%29%2F5
:
t(x) = %285%28sqrt%284%2Bx%5E2%29%29+%2B+4%28sqrt%28x%5E2-8x%2B17%29%29%29%2F20
The graph, time on the y axis

Minimum time, landing point: x = 2 mi from the coastal point nearest the boat,
:
Sorry I sent this prematurely by mistake. C