A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point. The visitor is planning to go from the tent to the rock formation. Suppose the visitor runs at a rate of 6 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the rock formation?

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Asked Nov 13, 2019
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A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point. The visitor is planning to go from the tent to the rock formation. Suppose the visitor runs at a rate of 6 mph and swims at a rate of 3 mph. How far should the visitor run to minimize the time it takes to reach the rock formation?

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Expert Answer

Step 1

Given A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is staying in a tent that is 4 miles west of that point.

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Rock formation
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W
S
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N Rock formation MEN E W S

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Step 2

Let,

x be the distance covered by running and y be the distance covered by swimming, so the figure will be

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4-х
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N 3 У E 4-х W х S

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Step 3

By using the Pythagoras...

y(4-x+(3)
y216+x2-8x +9
y2 x28x25
...1)
y x-8x25
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y(4-x+(3) y216+x2-8x +9 y2 x28x25 ...1) y x-8x25

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Calculus

Derivative

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