A man can row a boat at 8 km/h in still water. If the speed of the water current is 2 km/h and it takes him 2 hours to row to a place and come back, how far off (in km) is the place?

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Accepted Answer

Let the distance to the place be $$d$$.

1. **Speed downstream:** The man's speed in still water is 8 km/h, and the speed of the current is 2 km/h. Hence, the downstream speed is $$8 + 2 = 10 \, 	ext{km/h}$$.

2. **Speed upstream:** Similarly, the upstream speed is $$8 - 2 = 6 \, 	ext{km/h}$$.

3. **Total time for the trip:** The total time taken for rowing to the place and back is given as 2 hours. Using the formula for time ($$ 	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} $$), we set up the equation:  
   $$
   \frac{d}{10} + \frac{d}{6} = 2
   $$

4. **Solve for $$d$$:** To simplify:  
   $$
   \frac{3d + 5d}{30} = 2 \quad \Rightarrow \quad 8d = 60 \quad \Rightarrow \quad d = 7.5
   $$

Thus, the distance to the place is **7.5 km**.

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