A river flows at the rate of 3 mph downstream. It takes a person in a canoe the same time to row 22 miles downstream as it does or row 10 mi upstream. How fast can the person row in still water?

Sure, let's solve this step by step.

Step 1: Let's denote the speed of the person in still water as 'x' mph.

Step 2: The speed of the person when rowing downstream is the speed of the person plus the speed of the river, which is 'x + 3' mph.

Step 3: The speed of the person when rowing upstream is the speed of the person minus the speed of the river, which is 'x - 3' mph.

Step 4: The time it takes to row downstream 22 miles is the distance divided by the speed, which is '22 / (x + 3)' hours.

Step 5: The time it takes to row upstream 10 miles is the distance divided by the speed, which is '10 / (x - 3)' hours.

Step 6: According to the problem, the time to row downstream is the same as the time to row upstream. So we can set up the equation '22 / (x + 3) = 10 / (x - 3)'.

Step 7: Solve this equation for 'x'. You can do this by cross multiplying to get '22*(x - 3) = 10*(x + 3)'.

Step 8: Simplify this to get '22x - 66 = 10x + 30'.

Step 9: Rearrange to get '12x = 96'.

Step 10: Finally, solve for 'x' to get 'x = 8'.

So, the person can row at a speed of 8 mph in still water.