If the boat is moving in the direction of the stream that is called as downstream and If the boat is moving in the direction opposite to the direction of the stream that is called as upstream. So by using this technique, we solve the problems of boats and stream for AP Govt Jobs.
Speed of Boat in Still Water: ½ ()
Proof of Basic Formula
½ (Downstream Speed + Upstream Speed) = ½ [b + s + (b-s)] = ½ (2b) = b
Speed of Stream: ½ (Downward Speed – Upward Speed)
½ (Downward Speed – Upward Speed) = ½ [b + s – (b-s)] = ½ [b + s – b + s] = ½ (2 s} = s
- Usually the speed of boat would be greater than the speed of the stream.
- Downstream speed is always greater than the upward speed.
Please check the some examples of boats and streams
- A man can row a boat at 9 kmph in still water. He takes double the time to move upstream than to move the downstream – the same distance. Find the speed of the stream.
→Let the downward time = 1 hour and so the upward time = 2 hours.
→1/9+s = 2/9-s (Since distance is the same)
→18 + 2 s = 9 – s (By cross multiplication)
→18 – 9 = s + 2 s
→9 = 3 s
Hence s or Speed of stream = 9/3 = 3 kmph
→b + s = 2(b –s)
→i.e. b + s = 2b – 2s
→i.e. s + 2s = 2b –b Or
→b = 3s or 9 = 3s (b = 9 is given) = 3 kmph
- If a boat goes for 20 kmph along the stream and 10 kmph against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream.
→ Speed of Boat = ½ (20 + 10) = 15 kmph.
→ Speed of Stream = ½ (20 – 10) = 5 kmph.
→ Ratio: 15:5 = 3:1
- Find the time taken by the boatman to row 4 kilometres downstream and return to his starting point, if the speed or rate of stream is 2 kilometres per hour and the speed of the boat is 6 kilometers per hour.
ATQ (According to Question) and formula given above:
→ Time = Distance/Speed
→ Time taken = 4/6+2 + 4/6-2 = 4/8 + 4/4 = 0.5 + 1 = 1.5 Hour.
- If the speed of the stream is 2 km per hour, and the speed of the boat in still waters is 10 km per hour then find the time taken to cover 60 kms downstream.
→ 60/10+2 = 60/12 = 5 hours
- Find the speed of the stream if a boat used to takes 5 hours to travel 60 kms downstream at a rate of 10 kms per hour in still water.
→ Speed b + s = 60/5 = 12 kmph
→ Speed b = 10 kmph
→ so, speed s = 12-10 = 2 kmph
- A boat covers a certain distance in one hour downstream with the speed of 10 kmph in still water and the speed of current is 4 kmph. Then find out the distance travelled.