SOLUTION: A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstreams on the opposite bank, he first rows his boat to point P on the opposite ban

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Question 249420: A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstreams on the opposite bank, he first rows his boat to point P on the opposite bank and then walks the remaining distance x to B. He can row at a speed of 2 mi/h and walk at the speed of 5 mi/h. Where should he land so that he reaches B as soon as possible?
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A man stands at a point A on the bank of a straight river, 2 mi wide.
To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point P on the opposite bank and then walks the remaining distance x to B.
He can row at a speed of 2 mi/h and walk at the speed of 5 mi/h.
Where should he land so that he reaches B as soon as possible?
:
x = dist from p to b
The distance (d) rowed to point p is the hypotenuse:
d = sqrt%282%5E2+%2B+%287-x%29%5E2%29
d = sqrt%284+%2B+49+-+14x+%2B+x%5E2%29
d = sqrt%28x%5E2+-+14x+%2B+53%29
Time to row this dist at 2 mph
t = %28sqrt%28x%5E2+-+14x+%2B+53%29%29%2F2
:
Time spent walking at 5 mph = x%2F5
:
Total time (T): %28sqrt%28x%5E2+-+14x+%2B+53%29%29%2F2 + x%2F5
:
Graph this and find the minimum time

:
x = 6.1 mi; P to B (walking distance) Time rowing & walking; approx 2.3 hrs