A kayaker travels x miles per hour downstream for 4 hours. On the 6-hour return trip, the kayaker travels 2 miles per hour slower. How far did the kayaker travel in total?

speed downstream = x+2

speed upstream = x-2

4(x+2) = 6(x-2)

solve for x, then sub into 4(x+2) to get your distance

To find the total distance traveled by the kayaker, we need to calculate the distance for both the downstream trip and the return trip separately, and then add them together.

Let's start with the downstream trip. We are given that the kayaker travels at a speed of x miles per hour and the duration of the trip is 4 hours. The formula to calculate distance is:

Distance = Speed * Time

So, for the downstream trip:
Distance downstream = x miles per hour * 4 hours = 4x miles

Now, let's move on to the return trip. The kayaker travels at a speed of 2 miles per hour slower than the downstream trip. So, the speed for the return trip would be x - 2 miles per hour. The duration of the return trip is given as 6 hours. Applying the distance formula again, we get:

Distance return = (x - 2) miles per hour * 6 hours = 6(x - 2) miles

To find the total distance traveled, we add the distance downstream and the distance return:

Total distance = Distance downstream + Distance return
Total distance = 4x miles + 6(x - 2) miles

Now, we can simplify the equation:
Total distance = 4x + 6x - 12 miles
Total distance = 10x - 12 miles

So, the kayaker traveled a total distance of 10x - 12 miles.

Note: The answer to this question depends on the value of x, which is not provided. The expression 10x - 12 represents the total distance in terms of x.