Final answer:
To find the speed of a boat in still water when given its upstream and downstream travel distances and the speed of the current, set up an equation using the formula 'Time = Distance / Speed' for both scenarios and solve for the boat's speed. In this case, the speed of the boat in still water is 18 mph.
Step-by-step explanation:
Finding the Speed of a Boat in Still Water
To solve this problem, let's establish two scenarios: the boat traveling upstream and traveling downstream. When the boat goes upstream, its speed against the current is the boat's speed in still water minus the speed of the current. Conversely, when going downstream, the boat's speed is its speed in still water plus the current's speed. We are told the boat travels 55 miles upstream and 77 miles downstream in the same amount of time, and the current's speed is 3 mph. Let's use the variable b for the boat's speed in still water.
Upstream Speed: b - 3 mph
Downstream Speed: b + 3 mph
If the time taken for both trips is the same, we can set up the following equation:
Time = Distance / Speed
So, for upstream:
Time_upstream = 55 / (b - 3)
For downstream:
Time_downstream = 77 / (b + 3)
Since the times are equal:
55 / (b - 3) = 77 / (b + 3)
Now we solve for b which represents the speed of the boat in still water. By cross-multiplying and solving the equation:
55(b + 3) = 77(b - 3)
55b + 165 = 77b - 231
22b = 396
b = 18 mph
Therefore, the speed of the boat in still water is 18 mph.