# Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2 mph and can walk 5 mph. Where should she...

Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2 mph and can walk 5 mph. Where should she land her boat to reach the village in the least amount of time?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a straight shoreline from the point nearest the boat. She can row 2 mph and can walk 5 mph.

The distance of the village from her boat is `sqrt(2^2 + 5^2)` = `sqrt(4 + 25)` = `sqrt 29` miles.

Jane can walk at a speed 5 mph and row at 2 mph.

To reach the village in the least amount of time she should row for the least distance possible. For this, she has to row her boat straight along a line perpendicular to the shoreline.

She should land at a point where a line perpendicular to the shoreline meets it.