Its once again time for the Great River Race swim across the

It\'s once again time for the Great River Race, swim across the Panache River. If Karl fails to take the river\'s 1 mph current into account and he swims the race at 3 mph, how far from the finish marker does he end up when he makes it to the other side?

This is a question from my trig book precalculus 2nd edition by coburn, the answer is 1/6 but I do not know how to properly solve it. It is from the section about vectors and vector diagrams.

Solution

the race is across river => karl is swimming across river, though the water flow is along river.

let width of river = w miles

time to reach other end = width of river/speed of carl = w/3 hours

distance from finish marker = time x speed of river(water current) = (w/3) x 1 = w/3 miles

now, its necessary to know the river width to get the answer, if it is 1/6 then w must be 1/2.