A man can row a boat at the rate of 4km/hr in still water it takes 2 hours more to row the boat 6km upstream
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Step-by-step explanation:
Let the stream be flowing at s km/hr.
When rowing upstream, the boat moves at (4-s) km/hr.
When rowing downstream, the boat moves at (4+s) km/hr.
The time taken to row 2 km upstream = 2/(4-s) hr.
The time taken to row 2 km downstream = 2/(4+s) hr.
The total time taken to row both upstream and downstream = 2 hrs. Hence
2/(4-s) + 2/(4+s) = 2, or
1/(4-s) + 1/(4+s) = 1, or
4+s+4-s = (4-s)(4+s), or
8 = 16-s^2, or
s^2 = 8, or
s = 2√2
The stream flows at 2√2 km/hr.
Check: 2/(4-2√2 ) +2/(4+2√2) = 1.707106781 + 0.292893218 = 2. Correct.
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