There is an injured person on a boat on an island. A hospital is 43 miles inland and 10 miles south of the boat. A helicopter is at the hospital planning to come and rescue an injured person on the island. The boat travels 40 mph and the helicopter travels 120mph. What is the minimum distance traveled by the helicopter in order to minimize the time for the patient to get to the hospital?
I'm paraphrasing this problem, so hopefully you can understand what's being asked.
I don't know if this is how it's always done, but in my class we learned to set up a primary and secondary equation to solve the problem. Both equations have a common variable; in the secondary equation we solve for a certain variable, and substitute that value into the primary equation. Then we take the derivative of the primary equation and find the critical number(s) by setting the derivate equal to 0. I know how to do the algebra and derivatives, but I'm having trouble setting up the initial primary and secondary equations.
I know one of the equations must include the pythagorean theorem, a^2 + b^2 = d^2, with d being the distance. And I think the other equation has to do with distance = rate * time, but I'm not entirely sure how to use it. Can anyone offer some insight into how to set up this problem? What should the primary and secondary equation be?
I'm paraphrasing this problem, so hopefully you can understand what's being asked.
I don't know if this is how it's always done, but in my class we learned to set up a primary and secondary equation to solve the problem. Both equations have a common variable; in the secondary equation we solve for a certain variable, and substitute that value into the primary equation. Then we take the derivative of the primary equation and find the critical number(s) by setting the derivate equal to 0. I know how to do the algebra and derivatives, but I'm having trouble setting up the initial primary and secondary equations.
I know one of the equations must include the pythagorean theorem, a^2 + b^2 = d^2, with d being the distance. And I think the other equation has to do with distance = rate * time, but I'm not entirely sure how to use it. Can anyone offer some insight into how to set up this problem? What should the primary and secondary equation be?
