A kayaker is paddling at a steady rate for 10 miles with the river current. She can only travel 4 miles against the current in the same amount of time. If the rate of the current is 8 miles per hour, what is the kayaker's rate in still water (without the current) ?

Answer: 18.66 miles per hour.

Step-by-step explanation:

The velocity of the Kayak can be written as the velocity of the kayak in still water plus the rate of the current.

If K is the velocity of the kajak, and C the velocity of the current, we have that:

When the kajak moves along with the current, for a given time T.

(K + C) * T = 10mi

when the kajak move against the current:

(K - C) * T = 4mi

now we can replace C by 8mph, and take the quotient of both equations:

((K + 8mph) * T) / (K - 8mph) * T)) = 10mi/4mi

(K + 8) / (K-8) = 10/4

K + 8 = (K - 8) * 10/4

K + 8 = K*10/4 - 20

K*10/4 - K = K*6/4 = 20 + 8 = 28

K = 28*4/6 = 18.66

So the rate of the kajak is 18.66 miles per hour.