A boat 12 km downstream and comes back to the starting point in 3 hr. if the speed of the current is 3 km/hr,then the speed (in km/hr.) of the boat in still water is-

Let boat speed in still water = v km/hr. Downstream speed = v+3, upstream speed = v-3. Time = distance/speed, so 12/(v+3) + 12/(v-3) = 3. Solving: 12(v-3) + 12(v+3) = 3(v+3)(v-3) gives 12v - 36 + 12v + 36 = 3(v² - 9), so 24v = 3v² - 27, giving v² - 8v - 9 = 0, so (v-9)(v+1) = 0. v=9 km/hr (positive). Downstream: 12/12=1 hr, upstream: 12/6=2 hr, total 3 hr. ✓