Important Formulas on Boats and Streams :
Let us assume that the speed of the boat in still water is U km/hr and the speed of stream is V km/hr then, as mentioned above :
Speed downstream = (u+v)km/hr
Speed upstream = (u-v)km/hr
èIf the speed downstream is a km/hr and the speed upstream is b km/hr then :
Speed in still water = 1/2(a+b) km/hr
Rate of stream = 1/2(a-b)km/hr
SOME QUESTIONS ON BOATS AND STREAMS WITH SOLUTIONS:
(1)A man can row upstream at 8kmph and downstream at 10kmph. Find the man's rate in still water and the rate of current.
(2) A boat can travel with a speed of 12km/hr in still water . If the speed of the stream is 5km/hr , find the time taken by boat to go 68km downstream.
(3) If a man rows at the rate of 5kmph in still water and his rate against the current is 3.5kmph, then man's rate along the current is ?
(4) A boat covers a certain distance downstream in 1 hour, while it comes back in 3/2 hours. If the speed of the stream is 3kmph, what is the speed of the boaat in still water ?
(5) A speed of a boat in still water is 10 km/hr. If it can travel 26km downstream and 14km upstream in the same time , the speed of the stream is ?
(6)The speed of the boat in still water is 10km/hr and the rate of the current is 3 km/hr. The distance travelled downstream in 12 minutes is ?
(7)what is the speed of the boat in still water ?
(i)The speed downstream of the boat is twice the speed upstream.
(ii)The sum of the speeds of the boat , upstream and downstream is 12kmph
8.A man can row upstream at 5kmph and downstream at 15kmph .The speed of the stream is ?
(9)A boat takes a total time three hours to travel downstreams from P to Q and the upstream back from Q to P. what is the speed of boat in still water ?
i)The speed of the river current is 1 km per hour
ii)The distance between P and Q is 4 km.
(10) .A man takes twice long to row a distance against the stream as to row the same distance in favour of the stream .the ratio of the speed of the boat in still water is ?
ANSWERS WITH EXPLANATIONS
1. Solution : Rate in still water = 1/2 (10+8)km/hr = 9km/hr
Rate of current = 1/2(10-8)km/hr =1km/hr
2. Solution Speed downstream = (12+5)km/hr = 17 km/hr
Time taken to travel 68km downstream = 68/17hrs =4hrs
3. Solution: Let us consider the rate along the current be x kmph.
Then, 1/2(x+3.5) = 5 or X= 6.5 Kmph
4. Solution Let the speed of the boat in still water be x kmph.
Then speed downstream = (X+3)kmph
Speed upstraem = (x-3)kmph
Therefore (X+3)*1 = (x-3)*3/2
2x+6=3x-9 => X= 15kmph
5. solution : let the speed of the stream be x km/hr. then,
Speed downstream=(10+x)km/hr,
speed upstream= (10-x)km/hr
Therefore 26/(10+x)= 14/(10-x)
260-26x= 140+14x => 40x=120
x=3km/hr
6. solution : Speed downstream =(10+3)kmph= 13kmph
Distance travelled = 13*12/60 = 2.4 kmph
7. solution: Let the speed of the boat be x km/hr . Then
i) Speed downstream = 2x km/hr
ii)Says, the speed of the boat in still water = (1/2*12) = 6km /hr
8. Solution : Speed of the stream = 1/2 (15-5) = 5kmph
9. Solution : i) The speed of the current = 1km/hr
ii)PO =4km
let the speed of the boat in still water be x km/hr
4/(x+1) +4/(x-1) =3
10. solution : Let man's upstream be xkmph . then . his rate downstream =3x km/hr
(Speed in still water) : (Speed of stream ) = (2x+x/2) : (2x-x/2) =3x/2 : x/2
=> 3:1