Optimization Problem A walk in the park? Eva wants to get to the bus stop as qui

Question

Optimization Problem

A walk in the park? Eva wants to get to the bus stop as quickly as possible. The bus stop is across a grassy park, 2000 feet west and 600 feet north of her starting position. Eva can walk west along the edge of the park on the sidewalk at a speed of 6 ft/sec. She can also travel through the grass in the park, but only at a rate of 5 ft/sec (the park is a favorite place to walk dogs, so she must move with care). What path will get her to the bus stop the fastest? Remember, distance = rate x time.

Explanation / Answer

distance to be travellet on grass to reach busstop= squareroot of (2000^2 +600^2) =sqrt(4000000+360000)=2088ft

time =distance/rate

time needed on sidewalk =(2000+600)/6 =2600/6=433.33sec

time needed on grass =(2088)/5 =2600/6=417.6sec

417.6<433.33

so walking on grass will take her to busstop quickly

a)time needed on sidewalk =(2000+600)/6 =2600/6=433.33sec

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