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**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 â€“ y but down stream it will be x + y

**SOLVED EXAMPLES **

**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 **

- Let x be the speed of boat in still water and y be the speed of the stream

then x + y = 11

x â€“ 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? **

- Let x be the speed of boat and y be the speed of the stream.

Then x + y = 16

X â€“ y = 10 or 2x = 26 x = 13

2y = 6

y = 3

Speed of stream 3 km/hr

Shortcut: the speed of stream is (x â€“ y) / 2

or (16 â€“ 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 **

- if x is the speed of the man

And y is the speed of the current

The (x â€“ y) / 2 is the distance travelled by the stream in 5 hours.

Or (32 â€“ 17) / 2 = 15 / 2 = 7.5 km

So the speed of the current is 7.5/5 = 1 Â½ 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 â€“ 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. **

- let the speed of the motor boat in still water be x

So speed upstream = x â€“ 2

Speed down stream = x + 2

Or 240 x = 11 (x + 2) (x â€“ 2)

Or 240 x = 11x^{2} â€“ 44

Or 11x^{2} â€“ 240x â€“ 44 = 0

Or (11x + 2) (x â€“ 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. **

- Let the speed of stream be x km/hr. Speed down stream is (10 + x) km/hr

Speed up stream is (10 â€“ 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

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