Final answer:
To find the speed of the boat in still water, we need to establish equations based on the given data about the boat's upstream and downstream travel times and distances. However, additional information is needed to solve for the boat's speed in still water since we have two unknowns (the boat's speed and the current's speed) and require a second equation for a complete solution.
Step-by-step explanation:
The speed of the boat in still water can be determined by using the concept of relative speed. In the given problem, we have two scenarios where the boat travels upstream and downstream. The speed of the boat in still water is denoted by 'b', and the speed of the current is 'c'. While traveling upstream, the effective speed of the boat is 'b - c', and while traveling downstream, it is 'b + c'.
Let's take the first case where the boat travels 35 km upstream and 55 km downstream in 12 hours. Using the distances (d) and the times (t), we can create equations based on speed (d/t):
35/(b - c) + 55/(b + c) = 12 ------ Equation 1
Similarly, for the second case where the boat travels 30 km upstream and 44 km downstream in 10 hours, we have:
30/(b - c) + 44/(b + c) = 10 ------ Equation 2
To solve for 'b', we need a second equation relating 'b' and 'c', which is not provided directly in the problem. Usually, additional information about the speed of the current or one of the legs of the trip would be necessary to solve the system of equations and find the speed of the boat in still water.