Need help on Homework Asap please

Question

Simone is sitting on her towel at the beach. She wants to go to the snack shack. She can walk 1.5 feet per second in the sand and 2.3 feet per second on the sidewalk. Her towel is 22 feet away from the nearest point B along a straight boardwalk. The shake shack is 83 feet away from point B. (So the distance from B to C is 83 feet).If she walks in the sand along a straight line course to the sidewalk and then walks the rest of the way on the sidewalk, find an expression that computes the total time to reach the snack shack in terms of the location where Simone first reaches the sidewalk (so x = distance from B to where she first reaches the sidewalk).T(x) =   

Find the minimum time it takes for Simone to reach the snack shack. (I'm looking for the TIME here.)

DO NOT USE CALCULUS TO DO THIS.Minimum TIME required to get to snack shack =    seconds.(Round to the nearst second)

sketch graph when completed.

Answer 1

Hello Colin M.,

1) To begin, how would you represent the red length of the sidewalk in terms of x?

2) The distance from B to the towel is 22 so use the Pythagorean Theorem to find the hypotenuse of the right triangle with the legs of x and 22 which is also in red.

3) Answering questions 1 and 2 will give you the LENGTHS of the two red broken line segments. But you want minimum TIME not minimum length so you need to find the times that correspond to the two lengths. Since time equals distance/speed, you would divide each of your lengths by either 1.5 or 2.3. You can figure out which is which.

4) Then the time y = time on sand + time on sidewalk (your two answers to #3). You can sketch the graph of y and find the minimum value of y with a graphing calculator (2nd calc min) and this will be the answer without calculus.

If you work on this and want someone to check it, you can submit your work.