A man rows to a place 48 km distant and come back in 14 hours. He find...
Given information:
- Distance to the place: 48 km
- Total time taken: 14 hours
- Time taken to row 4 km with the stream = Time taken to row 3 km against the stream
Let's assume:
- Speed of the boat in still water = x km/hr
- Speed of the stream = y km/hr
Calculating time taken:
- Time taken to row 48 km downstream = 48 / (x + y) hours
- Time taken to row 48 km upstream = 48 / (x - y) hours
- Given, time taken to row 4 km with the stream = 4 / (x + y) hours
- Given, time taken to row 3 km against the stream = 3 / (x - y) hours
Forming equations:
- 48 / (x + y) + 48 / (x - y) = 14
- 4 / (x + y) = 3 / (x - y)
Solving the equations:
- Simplifying the first equation, we get: x = 5y
- Substituting x = 5y into the second equation, we get: y = 1 km/hr
Therefore, the rate of the stream is 1 km/hr.