An afternoon sightseeing cruise up river and back down river

An afternoon sightseeing cruise up river and back down river is schedualed to last 1 hour. The speed of the current is 4kh/h, and the speed of the riverboat in still water is 12km/h. How far upstream should the pilot travel before turning around?

Solution

total time alloted is 1 hour

speed of the current=4 kmph
speed of the boat=12 kmph

Upstream:
let the distance be x
speed=12-4 (since the boat and current will be in opposite directions)
=8 kmph
time=distance/speed=(x/8)hour

Downstream:
the distance will be equal to the distance it goes upstream
so distance=x
speed=12+4 (since boat and current will both be in the same direction)
=16 kmph
time=distance/speed=(x/16)hour

total time=(time upstream)+(time downstream)
1=(x/8)+(x/16)
1=(2x+x)/16
1=3x/16
16=3x
x=16/3 km

so he should go (16/3)km before turning around