SOLUTION: Alden, a passenger on a yacht moored 15 miles due north of a straight, east-west coastline, has become ill and has to be taken ashore in a small motorboat, which will meet an amb

Algebra ->  Angles -> SOLUTION: Alden, a passenger on a yacht moored 15 miles due north of a straight, east-west coastline, has become ill and has to be taken ashore in a small motorboat, which will meet an amb      Log On


   



Question 1073613: Alden, a passenger on a yacht moored 15 miles due north of a straight, east-west
coastline, has become ill and has to be taken ashore in a small motorboat, which will meet
an ambulance at some point on the shore. The ambulance will then take Alden to the
hospital, which is 60 miles east of the shore point closest to the yacht. The motorboat can
travel at 20 mph and the ambulance at 90 mph. In what direction should the motorboat
head, to minimize the travel time to the hospital? Express your answer using an angle.

Answer by ikleyn(52894) About Me  (Show Source):
You can put this solution on YOUR website!
.
The expression for the time is

t = %28sqrt%28x%5E2+%2B+15%5E2%29%29%2F20 + %2860-x%29%2F90

Where x is the distance along the straight east-west coastline.

You need to minimize it.

I didn't it. Instead, I prepared the plot below.




Plot y = %28sqrt%28x%5E2+%2B+15%5E2%29%29%2F20 + %2860-x%29%2F90