A boat travels 23 mph relative to the riverbank while going downstream and only 11 mph returning upstream. What is the boat's speed in still water?

v+c=23

v-c=11
========add
2 v = 34

v = 17 mph

To find the boat's speed in still water, we need to use the concept of relative velocity. The speed of the boat in still water can be denoted as X mph, and the speed of the river's current can be denoted as Y mph.

When the boat travels downstream, it moves with the current, so the effective speed increases. Therefore, the boat's speed relative to the water (downstream) is X + Y mph. Given that the boat's speed relative to the riverbank is 23 mph, we can write the equation:

X + Y = 23 ------(1)

Similarly, when the boat travels upstream, it moves against the current, so the effective speed decreases. Therefore, the boat's speed relative to the water (upstream) is X - Y mph. Given that the boat's speed relative to the riverbank is 11 mph, we can write the equation:

X - Y = 11 ------(2)

We now have a system of two equations with two variables (X and Y). We can solve this system of equations to find the values of X and Y.

To eliminate Y, we can add equations (1) and (2):

(X + Y) + (X - Y) = 23 + 11
2X = 34
X = 17

Now substitute the value of X back into equation (1) or (2) to solve for Y:

17 + Y = 23
Y = 6

Therefore, the boat's speed in still water is 17 mph.