The width of a river is $5\ m$ and in it water is flowing with a speed of $4\ m/min$. A boatman is standing on the bank of the river. He wants to sail the bat to a point at the other bank which is directly opposite to him, In what time will be cross the river, if he can sail the boat at $8m/min$, relative to the water?

To reach the point exactly opposite, the boatman must point the boat upstream to cancel the river's flow. The required upstream component of the boat's velocity must equal the river's speed of 4 m/min, and using the Pythagorean theorem with the boat's total speed of 8 m/min gives a perpendicular crossing component of the square root of (8 squared minus 4 squared), which is the square root of 48 m/min. The time taken to cross is the river width of 5 m divided by this perpendicular component. Dividing 5 by the square root of 48 gives a time of approximately 1.6 min.

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