# How long to swim across a river

A river is 300 m wide and the water flows downstream, exactly south, at 4 m/s. If a swimmer, moving at exactly 6 m/s, attempts to swim across the river:

At what direction should the swimmer orient himself to swim straight across the river in the east direction?

How long will it take the swimmer to across the river?

To swim straight across the river, the swimmer needs to compensate for the current pulling them downstream. Since the current flows south at 4 m/s and the swimmer can swim at 6 m/s, they must aim at an angle upstream, or to the north of east, to counteract the current. The swimmer should adjust their direction so that their velocity in the north-south direction exactly cancels out the 4 m/s flow of the river, leaving only their eastward velocity to move them straight across.

To find the time it takes to cross the river, use the swimmer's actual eastward speed, which is less than 6 m/s because part of their effort is spent countering the current. Once you know their eastward velocity, you can calculate the time to cross by dividing the river’s width, 300 m, by this velocity.

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