A kayaker paddles upstream from camp to photograph a waterfall and returns. The kayaker's speed while traveling upstream is 4 mi/h and downstream is 7 mi/h. What is the kayaker's speed in still water? What is the speed of the current?
Let the speed of the kayaker in still water be x mi/h and the speed of the current be y mi/h.
When paddling upstream, the kayaker's speed is x - y = 4 mi/h.
When paddling downstream, the kayaker's speed is x + y = 7 mi/h.
Solving these two equations simultaneously, we get:
x - y = 4
x + y = 7
Adding the two equations, we get:
2x = 11
x = 11/2
x = 5.5 mi/h
Substitute x back into one of the equations to find y:
5.5 - y = 4
y = 5.5 - 4
y = 1.5 mi/h
Therefore, the kayaker's speed in still water is 5.5 mi/h and the speed of the current is 1.5 mi/h.