Question

A boat takes a total of 6 hours to row 8 kms downstream and to return back to the starting point. if the speed of the boat is 3 kmph, for how much time was the boat moving downstream and how much time upstream ?

Answer 1

Total distance be 8+8=16 hr
let the speed of the stream be x
speed of boat =3kmph
so, speed in downstream =x+3 kmph
speed in upstream=3-x kmph

time taken in downstream=8/x+3
time taken in upstream=8/3-x
as total time =6
so, 6=8/3+x +8/3-x
so, 6=8(3-x)+8(3+x)/(3+x)(3-x)
so, 6(9-x^2)=24-8x+24+8x=48
so, 54-6x^2-48=0
so, 6=6x^2
so, x=√6/6=1

hence time in upstream=8/3-1=4hr
time in downstream=8/3+1=2 hr

Thanks.