1. Boats and Streams

2. BOATS – 1
• Generally the speed of the boat means the
speed of the boat in still water.
• Similarly the speed of the swimmer means
the speed of the swimmer in still water.

3. BOATS - 2
• UPSTREAM If the boat (or the swimmer)
moves against the stream, then it is called
upstream. If the speed of the boat (or the
swimmer) is x and the speed of the stream is
y, then upstream speed = x – y.
• DOWNSTREAM If the boat (or the swimmer)
moves with the stream, then it is called
downstream. If the speed of the boat (or the
swimmer) is x and the speed of the stream is
y, then downstream speed = x + y.

4. BOATS – 3

5. BOATS - 4
Theorem 1.
• A man can row x km/h in still water. If in a
stream which is flowing at y km/h, it takes
him z hours to row to a place and back, the
distance between the two places is
2 2
2
z x y
x

6. BOATS - 5
• A man can row 12 km/h in still water. If the
speed of the stream is 8 km/h, if it takes 3
hours to row to a place and back, find the
distance between two places.
• Here x = 12. Y = 8 and z = 3.
• So the distance is 10 km.

7. Boats – 5a

8. BOATS - 6
Theorem 2.
• A man can row a certain distance
downstream in x hours and returns the same
distance in y hours. If the stream flows at
the rate of z km/h, then the speed of the man
in still water is given by
z x y
y x

9. Boats – 6a

10. BOATS – 7

11. BOATS – 8
• Example A man swims
downstream 15 km and upstream
9 km, taking 3 hours each time.
What is the velocity of current?
• Velocity of current = 1km/hr 15 9
2 3

12. BOATS - 9
• A man can row 12 km/h in still water. He takes thrice as
long to row up as to row down the river. Find the rate of
the stream.
• Rate of the stream =
2
1
Speed of manin still water
No of times to row up as to row down
13
122
= 6 km/h.

13. BOATS -10
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 (in km/hr) is
a) 3
b) 5
c) 8
d) 9

14. BOATS -11

15. BOATS – 12
• A man can row upstream at 8 kmph and
downstream at 13kmph. The speed of the
stream is
a) 2.5kmph
b) 4.2 kmph
c) 5 kmph
d) 10.5 kmph.

16. BOATS - 12

17. BOATS – 13
A man rows downstream 32 km and 14km
upstream. If he takes 6 hours to cover each
distance, then the velocity (in kmph) of the
current is
a) 0.5
b) 1
c) 1.5 d) 2

18. BOATS – 13
A man rows downstream 32 km and 14km
upstream. If he takes 6 hours to cover each
distance, then the velocity (in kmph) of the
current is a) 0.5 b) 1 c) 1.5 d) 2
Rate downstream =
6
32
kmph; Rate upstream =
6
14
kmph.
Speed in still water =
6
14
6
32
2
1
kmph =
2
3
kmph = 1.5 kmph.

19. BOATS - 14
• 1)A boat running downstream covers a
distance of 16km in 2 hours while for
covering the same distance upstream, it
takes 4 hours. What is the speed of the boat
in still water? a) 4km/hr b) 6 km/hr c) 8
km/hr d) Data inadequate.

20. BOATS – 14
• A boat running downstream covers a distance of 16km in 2
hours while for covering the same distance upstream, it
takes 4 hours. What is the speed of the boat in still water?
a) 4km/hr b) 6 km/hr c) 8 km/hr d) Data inadequate.
Rate downstream =
2
16
kmph = 8 kmph; Rate upstream =
4
16
kmph = 4 kmph.
Speed in still water = 48
2
1
kmph = 6 kmph.

21. BOATS – 15
If a man rows at the rate of 5 kmph in still
water and his rate against the current is 3.5
kmph, then the man’s rate along the current
is a) 4.25 kmph b) 6 kmph c) 6.5 kmph
d) 8.5 kmph

22. BOATS – 15
If a man rows at the rate of 5 kmph in still water and his
rate against the current is 3.5 kmph, then the man’s rate
along the current is a) 4.25 kmph b) 6 kmph c) 6.5 kmph
d) 8.5 kmph
Let the rate along the current be x kmph. Then,
53.5
2
1
x x = 6.5 kmph.