Celine paddles a kayak 4 miles upstream in 2 hours. The return trip downstream takes her half an hour. What is the rate that Celine paddles in still water? What is the rate of the current?

Step-by-step explanation:

We can use the relationship ...

   speed = distance/time

along with the variables k = kayak rate, c = current rate, to write the equations ...

  4 mi/(2 h) = k - c

  4 mi/(1/2 h) = k + c

Adding these equations together, we get ...

  2 mi/h + 8 mi/h = 2k

  k = 5 mi/h . . . . . . . . . . . divide by 2 and simplify

Subtracting the first equation from the second, we get ...

  8 mi/h -2 mi/h = 2c

  c = 3 mi/h . . . . . . . . . . . divide by 2 and simplify

Celine paddles 5 mi/h in still water. The rate of the current is 3 mi/h.