Final answer:
To find the rate of the boat in still water, we can use the concept of velocity addition. The rate of the boat in still water is 0 mph.
Step-by-step explanation:
Physics: Finding the Rate of a Boat in Still Water:
To find the rate of the boat in still water, we can use the concept of velocity addition. Let's assume the rate of the boat in still water is 'b' mph.
When the boat is traveling upriver against the current, the effective velocity is the boat's rate in still water minus the rate of the current. So, the upriver velocity is 'b - r' mph. On the return trip downstream with the current, the effective velocity is the boat's rate in still water plus the rate of the current. So, the downstream velocity is 'b + r' mph.
Since the distance traveled on both trips is the same, we can set up an equation:
2d / (b - r) = 2d / (b + r)
Cross multiplying gives:
(b + r) * 2d = (b - r) * 2d
Simplifying further, we get:
b + r = b - r
2r = 0
r = 0
Therefore, the rate of the boat in still water is 'b = 0' mph.