6. Two fishing boats have the same average speed in still water. They leave a dock at the same time. One boat heads upstream and the other heads downstream. At a certain point, boat A is $56 \mathrm{~km}$ downstream and boat $B$ is $24 \mathrm{~km}$ upstream. The average speed of the current is $8 \mathrm{~km} / \mathrm{h}$. What is the average speed of the boats in still water?
Answer
Final Answer: The average speed of the boats in still water is \(\boxed{20}\) km/h.
Step 1 ：Let the average speed of the boats in still water be x km/h. Since boat A is going downstream, its effective speed will be (x + 8) km/h. Boat B is going upstream, so its effective speed will be (x - 8) km/h.
Step 2 ：Let t be the time taken for both boats to reach their respective positions. Then, we can write the following equations:
Step 3 ：For boat A: \(56 = (x + 8) \times t\)
Step 4 ：For boat B: \(24 = (x - 8) \times t\)
Step 5 ：We can solve these equations simultaneously to find the value of x.
Step 6 ：Final Answer: The average speed of the boats in still water is \(\boxed{20}\) km/h.
