Chapter - 17
BOATS AND STREAMS
POINTS TO KNOW AND REMEMBER
i) When speed of boat is given, it means the speed of the boat in still water.
ii) Upstream means that the boat or a person in moving against the flow of water and downstream means in the direction of the flow of water.
iii) if x and y are the speeds of the boat and speed of the stream / river respectively then the relative or effective speed of boat with respect to the stream if it moves upstream is x – y but down stream it will be x + y
Example 1. In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water is
then x + y = 11
x – y = 5 or 2x = 16or x = 8km/hr.
shortcut = Add the two speed, and divide by 2
i.e. speed of boat in still water = (11 +5) / 2 = 8 km/per hr.
Example 2: A man can row upstream at 10 km/hr and down stream 16 km/hr the speed of the stream is?
Then x + y = 16
X – y = 10 or 2x = 26 x = 13
2y = 6
y = 3
Speed of stream 3 km/hr
Shortcut: the speed of stream is (x – y) / 2
or (16 – 10) / 2 = 3 km/hr
Example 3: A man rows upstream 32 km and down stream 17 km. If to row the same distance upstream and down stream he takes 5 hours (in each direction) the velocity of the current is
And y is the speed of the current
The (x – y) / 2 is the distance travelled by the stream in 5 hours.
Or (32 – 17) / 2 = 15 / 2 = 7.5 km
So the speed of the current is 7.5/5 = 1 ½ km/hr
Example 4: There is a road beside a river. Two friends start from a place A and reach a point B and come back again to A. One of them moves at a speed of 12 km/hr on a bicycle while the other sails on a boat at a speed of 12 km/hr. If the river flows at a rate of 4 km/hr which of the two friends will reach to place A first.
Since the cyclist moves both ways at the speed of 12 km/hr. so his average speed is 12 km/hr.
The boat sailor moves downstream at a speed of 12 + 4 = 16 km/hr
And moves upstream at a speed of 12 – 4 = 8 km/hr
His average speed can be found by Harmonic mean
Average speed =
Since the average speed of the cyclist is more so he will reach back at A first.
5. Speed of a stream is 2 km/hr. A motor boat goes upstream upto a distance of 8 km upstream and reaches back at the starting point in 44 minutes. Find the speed of the motor boat in still water.
So speed upstream = x – 2
Speed down stream = x + 2
Or 240 x = 11 (x + 2) (x – 2)
Or 240 x = 11x2 – 44
Or 11x2 – 240x – 44 = 0
Or (11x + 2) (x – 22) = 0
Or x = 22
So speed of the motor boat in still water = 22 km/hr
6. The speed of a boat in still water is 10 km/hr. if it can travel 26 km down stream and 14 km upstream in the same time, what is the speed of the stream.
Speed up stream is (10 – x) km/hr
So 26/(10+x) =14/(10-x) or 260-26 x = 140+14x
Or 40 x = 120 x = 3
So speed of stream is 3 km/hr