If you can swim in still water at 0.5m/s, the shortest time it would take you to swim from bank to bank across a 20m wide river, if the water flows downstream at a rate of 1.5m/s, is most nearly:

42.55 seconds

Explanation:

Check attached file for the diagram.

Vr= velocity of the river, if the water flows downstream, which is equal to 1.5m/s(from the question), Vb= my velocity at angle alpha which is perpendicular to the x-axis, and c= distance to swim from river bank to the other river bank.

Therefore, the shortest time to be taken to swim or cross the river,t=river with width of C÷ vertical component Vj.

Note that (vector) Vj= (vector)Vr+(vector)Vb.

Also, alpha must be maximum and for that to happen it must have a value of one(1).

Hence, time taken to cross the river,t= C/Vb× sin (alpha).

t= 20m÷ 0.5 ×sin 90.

t= 20÷ 0.47.

t= 42.55 seconds.