A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

A sailor can row a boat 8 km downstream and return back to the startin

1.	A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.
Answer» Let the speed of the boat in still water be x km/hr. Speed of the stream = 2 km/hr. `:." ""speed downstream"=(x+2)km/hr,` speed upstream `=(x-2)km/hr.` Time taken to cover 8 km downstream and return back to the starting point `=(8)/((x+2))+(8)/((x-2))`. But, this time is given as `1(40)/(60)` hours `=1(2)/(3)" hours "=(5)/(3)` hours. `:." "(8)/(x+2)+(8)/(x-2)=(5)/(3)` `implies" "(1)/(x+2)+(1)/(x-2)=(5)/(24)implies((x-2)+(x+2))/((x+2)(x-2))=(5)/(24)` `implies" "(2x)/((x^(2)-4))=(5)/(24)implies5x^(2)-20=48x` `implies" "5x^(2)-48x-20=0implies5x^(2)-50x+2x-20=0` `implies" "5x(x-10)+2(x-10)=0implies(x-10)(5x+2)=0` `implies" "x-10=0" or "5x+2=0` `implies" "x=10" or "x=(-2)/(5)` `implies" "x=10" "[because" speed of the boat cannot be negative"]` Hence, the speed of the boat in still water is 10 km/hr.