Boat & Stream

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find  the time taken by the boat to go 68 km downstream. Answers: Speed downstream = (13 + 4) km/hr = 17 km/hr. Time taken to travel 68 km downstream = 68 hrs = 4 hrs. 17 A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is: Answers: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr. Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? Answers: Let the man's rate upstream be x kmph and that downstream be y kmph. Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs. x x 8 4 = (y x 4) 5 44 x =4y 5  y = 11 x. 5  Required ratio = y + x : y - x 2 2    = 16x x 1 : 6x x 1 5 2 5 2    = 8 : 3 5 5    = 8 : 3. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is: Answers: Let the speed of the stream be x km/hr. Then, Speed downstream = (15 + x) km/hr, Speed upstream = (15 - x) km/hr. 30 + 30 = 4 1 (15 + x) (15 - x) 2 900 = 9 225 - x2 2  9x2 = 225  x2 = 25  x = 5 km/hr. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is: Answers: Speed in still water =1(11 + 5) kmph = 8 kmph