Question

A boatman goes 6km upstream and back again to starting point in 2 hours. If the speed of water is 4 km/hours. Find the speed of boat?

Answer 1

let the speed of the boat in still water is x km/hr
& the current of the stream runs at the rate of 4Km/h
so in upstream the boat goes at (x+4)km/hr
so time taken to move 6 km =6/(x+4)hr
so in downstream the boat goes at (x-4)km/hr
so time taken to move 6 km =6/(x-4)hr
total time 6/(x+4)+6/(x-4)=2
or 6[(x-4)+(x+4)]=2(x+4)(x-4)
or 6x=x^2-16
or x^2-6x-16=0
or x^2+2x-8x-16=0
or x(x+2)-8(x+2)=0
or (x+2)(x-+8)=0
or x=-2 or 8
so the speed of the boat in still water is 8 km/hr