A kayaker spends a morning paddling on a river. She travels 9 miles upstream and 9 miles downstream in a total of 6 hours. In still water, she can travel at an average speed of 4 miles per hour. What is the average speed of the river's current in miles per hour?

A) 1 mi/h

B) 2 mi/h

C) 3 mi/h

D) 1.5 mi/h

To answer this item, we have 4 as the speed of the kayaker in still water and the speed of current be y.

When the karayaker moves upstream or against the current, his speed would be 4 - y. Further, if he moves downstream or with the current, the total speed would be 4 + y. The time utilized for the travel is equal to the ratio of the distance and the speed.

Total time = 9 / (4 - y) + 9 / (4 + y) = 6

We multiply the equation by (4-y) (4+y)

9 (4-y) + 9 (4 + y) = 6 (4-y) (4+y)

Simplifying,

72 = 96 - 6y²

Transposing all the constants to only one side of the equation and rearranging,

6y² = 96 - 72

y² = 4

y = 2

Hence, the speed of the river's current is 2 miles/hr. The answer is letter B.) 2 miles/hour.