The current of a stream runs at 1km/hr. A motor boat goes 35 km. upstream and back again to the starting point in 12 hours. The speed of motor boat in still water is :
6 km/hr
7 km/hr
8.5 km/hr
8 km/hr
Explanation:
Let the speed in still water be x km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12
⇒ 35(2x) = 12(x2 - 1)
⇒ $12x^{2} - 70x - 12$ = 0
⇒ $12x^{2} - 72x + 2x - 12 $ = 0
⇒ 12x(x - 6) + 2 (x - 6) = 0
⇒ (x - 6) (12x + 2) = 0
∴ x = 6 km/hr
Let the speed in still water be x km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12
⇒ 35(2x) = 12(x2 - 1)
⇒ $12x^{2} - 70x - 12$ = 0
⇒ $12x^{2} - 72x + 2x - 12 $ = 0
⇒ 12x(x - 6) + 2 (x - 6) = 0
⇒ (x - 6) (12x + 2) = 0
∴ x = 6 km/hr