Suppose that you are at point A and want to get to point C on the other side of the river.

Question

Suppose that you are at point A and want to get to point C on the other side of the river.

You can either row your boat from point A to point C. Or, you can row from point A to some point P between B and C, and then run the rest of the way to point C.

If you row at an average rate of 3 km/h and run at an average rate of 5 km/h, what is the shortest amount of time it will take you to get to point C?

Group of answer choices

3.733 hours

3.750 hours

4.333 hours

4.067 hours

None of these

Answer 1

x = BP

T(x) = time to travel AP + PC = AP/3 + PC/5

AP = √(5² + x²)

PC = 12 - x

So you have to minimize T(x) = (1/3)√(5² + x²) + (12 - x)/5 over the interval 0≤ x ≤12.

The minimal value of T(x) will be your answer.