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A man launches a boat from point A, which is on the bank of a finger-shaped lake that is 3 km wide. Point C is 3 km east of point A. The man wants to reach point B as quickly as possible. Point B is on the opposite bank of the lake and 8 km south of point C. He has three options:

  1. Row directly across the lake from point A to point C, leave his boat, and then jog along the shore from point C to point B.
  2. Row directly from point A to point B along a diagonal.
  3. Row to some point D part way down the shore, leave his boat, and jog the rest of the
    way to point B.

The man can row at a speed of 6 km/hr and can jog at a speed of 8 km/hr.

The diagram of this situation is given below.

Find the time it would take to row from A to C and then jog from C to B.

Of the choices provided, find the distance between point C and point D that would give the smallest total time for this journey.

Time for A to C to B path

Position of D to minimize time

1.0

1.5

2.0

2.5

3.0

3.5

4.0

8.0

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