Question

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

Answer 1

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.