# Optimizing Time

**Problem:**Maya is 2 km offshore on a boat and wishes to reach a coastal village which is 6 km down the straight shoreline from the point on the shore nearest to the boat. She can row at 2 km/hour and run 5 km/hour. Where should she land her boat to reach the village in the least amount of time? To get an idea of what this question is asking drag the point P along the shoreline to see how the total time taken to complete the trip changes.

Read the problem at the top of the page.

- Drag P to 0 (the longest distance). How long does it take to get to the house?
- Drag P to 6 (the shortest distance). How long does it take to get to the house?
- Explain why the above are the shortest and longest distances?
- Use the applet to find the shortest time to get to the house. Check with the "optimal traveler". Were you correct?
- Let the distance from (0, 0) to P be x, what is the distance to the house from P?
- Based on the given rate, how long does it take to travel this distance. Recall that
- Find an equation, in terms of x, for the time it takes to travel the dashed blue line.
- Find an equation for the total time it takes to travel to the house.

Thanks to J Mulholland for creating the applet and question.

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