In order for this problem to have a unique solution, we must assume that the current must not alter the kayaker's speed of 4 miles per hour relative to the water; in other words, his speed relative to the shore of the river must also be 4 miles per hour. Under this assumption, we can find the solution as follows: First, we split the vector representing the kayaker's velocity into its rectangular components. 4 miles per hour at an angle of N60E means the vector has length 4 and makes an angle of 30 degrees with the positive x-axis, which is the East line when the problem is placed into a rectangular coordinate system. This means the components of the vector are (4 cos 30°)i + (4 sin 30°)j = 3.464i + 2j. The current must be such that it changes the kayaker's velocity relative to the shore to (4 cos 20°)i + (4 sin 20°)j = 3.759i + 1.368j. Subtracting, we find that the rectangular components of the current must be 0.295i - 0.632j. Putting those back into polar form, the current must be 0.7 miles per hour in the direction of S25E (rounding to the precision specified in the problem).
