Swimming in a river

the two vectors of motion, you swimming across, and the river pulling you down are independent.

at 1 meter per second you will swim across in thirty seconds

in thirty seconds, and .5 meters per second the river will pull you down 15 meters

The total time = Total distance covered / Total speed.

So, to get to the other side it should take $\frac{30m}{1m/s} \implies 30s$

In $30s$ the river will carry downriver $0.5m/s \times 30s \implies \boxed{15m}$

The time it takes to cross the river is $30\text{ m}\div 1\text{ m/s}=30\text{ s}$ .

In this time, the current carries you $0.5 \text{ m/s}\times 30\text{ s}=\boxed{15 \text{ m}}$ .

For every one meter we swim forward we get pushed 0.5 m to the right. so when we move 2m forward we get pushed 1m right. so when we move 30m forward we get pushed 15m right.

The distance across river is 30m.The speed that we across the river is 1metre in each second(1m/s). While the current in the river will carries us downriver in the speed of 0.5 metre in each second.We need 30 second to reach the destination .So, we use the time taken to across the river times the distance that the current carries us down river x time taken=30x0.5

time taken to across the river=30s

distance that carries us downriver =0.5m in 1 second

distance of downrivers=30x0.5

                                       =15m

To cross 30m @ 1m/s it takes 30 seconds. By this time the river would have taken you 30s* 0.5m/s = 15 meters free of cost! Thus the answer.

river 30m wide we are swimming at 30m/s the current in the river is 0.5m/s so ,every meter you swim towards the other side the current in the rivers drags you 0.5m down river since the width is 30 m so you are downriver 15 m ,simple unitary method.

in every 1 m/s, there is 0.5 m/s downriver, since the river is 30m wide, 30*0.5=15m :D