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| Math Central | Quandaries & Queries |
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Question from Christy, a student: Hello, I have no idea where to start with this question. Bob is at point B, 35 miles from A. Alice is in a boat in the sea at point C, 3 miles from the beach. Alice rows at 2 miles per hour and walks at 4.25 miles per hour, where along the beach should she land so that she may get to Bob in the least amount of time? |
Hi Christy,
I think the problem should say "Alice is in a boat in the sea at point C, 3 miles from the closest point A on the beach." here is my diagram
Alice is to row from C to some point P on the beach and then walk along the beach to Bob.
Put a coordinate system on the diagram with the origin at B and with the shoreline being the X-axis. C has coordinates (35, 3). Let P have coordinates (x, 0). Use the distance formula to write an expression for the distance from C to P. How long does it take Alice to row from C to P? How long does it take her to walk from P to B? What is her total time? Use the calculus you know to find the value of x that minimizes this time.
Penny
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