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jlulu2738
jlulu2738
30.03.2020 • 
Mathematics

A street is 10 yards wide. You are at the curb at the point A. The point B is directly across the street from you, at the opposite curb, 10 yards from you. The point C is 50 yards down the street from point B, also at the curb across and down the street from you. You want to go from point A to point C as rapidly as possible. You must walk when you are in the street, and your walking pace is 2 yards per second. But you can run when you are on the sidewalk --- the line between points B and C --- and your running pace is 4 yards per second. One possibility is to cross the street orthogonally from A to B (walking) and then run down the sidewalk from B to C. Another possibility is to slant across the street on a straight line from A to C, though you must walk the entire way. (Don't worry about traffic; there are no cars coming to interfere with your crossing. Still, you must walk when in the street.) Then an idea occurs to you: You could walk from A to a point D on the opposite side of the street, with D somewhere in between B and C. Then you can run the rest of the way from D to C. Does this idea allow you to save time, compared with the two possibilities in the first paragraph

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