Alberta went on a kayaking trip. She traveled 2 miles upstream in the same amount of time that she spent kayaking 6 miles downstream. The water's current was 2 miles per hour. What was her average rate of speed?

4 mph

Step-by-step explanation:

Givens

Current = c = 2 mph

Alberta = r = ?

d = 2 mph upstream

d1 = 6 mph downstream

Formula

d = r * t

The time is the same so the formula becomes d/r = t

2 / (r - 2) = 6 / (r + 2)

Solution

Cross Multiply

2 * (r + 2) = 6 * (r - 2)

2r + 4 = 6r - 12 Subtract 2r from both sides

4 = 6r - 2r - 12 Combine the right.

4 = 4r - 12 Add 12 to both sides.

4 + 12 = 4r

16 = 4r Divide by 4

16/4 = 4r/4

r = 4

Alberta's rate of travel is 4 mph