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You are a lifeguard and spot a distressed child 70 meters along the shore and...

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Calculus

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You are a lifeguard and spot a distressed child 70 meters along the shore and 40 meters from the shore to the child You run along the shore and for a while and then jump into the water and swim from there directly to child You can run at a rate of 4 meters per second and swim at a rate of 1 2 meters per second How far along the shore should you run before jumping into the water in order to get to the child in the least amount of time Round your answer to three decimal places Hint Consider this diagram where a represents the distance running and y represents the distance swimming Try to write y in terms of x and use that to build the time as a function of x child you X 70 y 40

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