How wide is the river?

I get the impression that there is some trick in this question that I have not picked up on as yet. But let me bite.

v = speed of boat in still water.

Across the river, v = component of velocity normal to current assuming that he aims directly across the river.

v - 3 = net speed up the river

Thus v - 3 = v/2

v = 6 m/s

The river is 6 * 120 = 720 m wide

Down the river, his net speed is 9 m/s which takes 80 sec.

***

Note the minimum time to cross the river comes from maximizing the component of his net speed across the river. If he wants to end up traveling directly across the river, he needs to aim slightly upstream, which means his net cross river component will be less than v. However if he aims directly cross river, he ends up slightly down river, but his cross river component is maximized. I assume that is what takes 2 mins.

***EDIT

OK, in that case, his speed across the river is √(v^2 - 3^2) while is speed up the river is v-3

We require √(v^2 - 3^2) = 2(v-3)

solve to get v = 5 m/s

This would make the river 600 m wide.

Down the river, it takes 1 min.

The time to go up the river is 2(time to cross) the river, so

speed upriver = 1/2 speed across river

speed upriver = (speed across river) - 3m/s

Speed across river = 6 m/s

width of river = 6 m/s x 60s/min x 2 min = 720 m

Speed downriver = 3 m/s + 6m/s = 9 m/s

Time to travel 720 m downriver = 80 s

You can get the same answer by seeing that speed downriver = 3/2(speed across river), so time downriver = 2/(3/2) = 4/3 min = 80 s

d = VxT

d = 120V

d = 240( V - 3)

V =2V - 6

V = 6 m/s

d = 6 x 120 = 720 m

720 = 9T

T = 80 sec