## BOATS SET4

1. Man can row 30km upstream & 44km downstream in 10 hrs. Also he run 40km upstream & 55km downstream in 13 hrs. Find the rate of the current & the speed of the man in still water ?A) 3 & 8 km/hrB) 2 & 5 km/hrC) 1 & 3 km/hrD) None of the aboveAns. AUpstream Downstream time30 44 1040 55 13Upstream = 30*55 – 40*44 / 44*13 – 55*10 = 5Downstream = 30*55 – 40*44 / 30*13 – 40*10 = 11Therefore, Rate of current = 11-5/2 = 3 km/hrSpeed of the man = 11+5/2 = 8 km/hr 2. A motor boat takes 2 hrs to travel a distance of a 9km down the current & it takes 6 hrs. to travel the same distance against the current. The speed of the boat(in km/hr) in still water & that of the current are A) 3,2B) 3,1C) 3.5,2.5D) 3,1.5Ans. DLet speed of boat in still water be x km/hr & speed of current be y km/hr9/x+y = 2& 9/ x-y =6X+y=9/2x-y = 9/6 = 3/2therefore, x=3 & y=1/2 km/hr 3. A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.A) 4 hoursB) 5 hoursC) 6 hoursD) 7 hoursAns. ASpeed downstream = (16 + 5) = 21 kmph Time = distance/speed = 84/21 = 4 hours 4. A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.A) 0.4 kmB) 1.4 kmC) 2.4 kmD) 3.4 kmAns. CLet the distance is x kmRate downstream = 5 + 1 = 6 kmphRate upstream = 5 – 1 = 4 kmphthen x/6 + x/4 = 1 [because distance/speed = time]=> 2x + 3x = 12 => x = 12/5 = 2.4 km 5. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes isA) 1.6 kmB) 2 kmC) 3.6 kmD) 4 kmAns. CSpeed downstreams =(15 + 3)kmph= 18 kmph.Distance travelled = (18 x 12/60)km= 3.6km iibm