158E- Boats and Streams

Boats and Streams Explained

1. Downstream/Upstream:

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

2. If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u - v) km/hr.

3. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water =	1	(a + b) km/hr.
	2

4.  

Rate of stream =

1

(a - b) km/hr.

Problems on boats and streams

1. If a man can swim downstream at 6kmph and upstream at 2km ph his speed in still water is :

Ans :4 km/hr

Basic Formula:

If the speed download stream is a km/ hr and the speed upstream is 6 km/ hr then Speed in still water is = ½ (a+b) km / hr

Answer with Explanation:

Given : speed downstream a = 6 km ph

Speed upstream b = 2kmph

Speed in still water = ½ (a+b) kmph

= ½ (6+2)

= 8/2 = 4kmph

speed in still water = 4kmph

2. A man can row upstream at 8kmph and downstream at 12kmph the speed of the stream is

Ans:  2.5km/hr

Basic Formula:

If the speed downstream is a kmph and the speed upstream is 6 kmph then Speed of the stream = ½ (a-b) kmph

Answer with Explanation:

Speed downstream a = 12kmph

Speed upstream b = 8 kmph

Speed of the stream = ½ (a-b) = ½ (12-8)

= 4/2 = 2 kmph

speed of the stream = 2kmph

3. If Anshul rows 15km upstream and 21km downstream taking 3 hours each time, then the speed of the stream is

Ans: 1km/hr

Basic Formula:

Speed of the stream = ½ (a-b) where

a= speed downstream

b= speed upstream

Answer with Explanation:

Speed downstream = distance travelled / time taken = 21/3

a = 7km / hr

speed upstream = 15/3 =5

b = 5km/hr

speed of the stream = ½ (a-b) km/hr

= ½ (7-5)

= 1 km/hr

speed of the stream = 1km/ hr

4. A man rows 750m in 675 seconds against the stream and returns in 7 ½ minutes. How rowing speed in still water is

Ans: 5km/hr

Basic Formula:

i) Speed in still water = ½ (a+b) kmph where ‘a’ is speed downstream and ‘b’ is speed upstream

ii) a km / hr = a x 5/18 m /s

iii) a m/sec = a x 18/5 km/hr

Answer with Explanation:

Speed upstream ‘b’ = 750m / 675 sec = 30/31 m/sec

Speed downstream ‘a’ = 700/ 7 ½ m / minutes

a = 750/ 450 m / sec = 5/3 m/sec

speed instill water = ½ (a+b)

= ½ (750/450 + 750/675 ) m /sec

= ½ (750/450 + 750/675 ) x 18/5 km/hr

= ½ (5/3 + 30/31) x 18/5 km/hr

= 4.7 km/hr

5. A man rows 13km upstream in 5 hours and also 28km downstream in 5 hours. The velocity of the sream is

Ans:  1.5 km/hr

Basic Formula:

Velocity of the stream = ½ (a-b) km/hr

Answer with Explanation:

Speed upstream ‘b’ = 13km/ 5 hr

Speed downstream ‘a’ = 28/5 km/hr

Velocity of the stream = ½ (a-b)

= ½ (28/5 – 13/5)

= ½ (15/5)

= 3/2

velocity of the stream = 1.5 km/ hr

6. If a boat goes 7km upstream in 42 minutes and the speed of the stream is 3kmph, then the speed of the boat in still water is

Ans:  13km/hr

Basic Formula:

i. speed of the stream = ½ (a-b) km/hr

ii. speed of the boat in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed upstream = 7/42 km/min = 7/42 x 60 km/ hr

i.e, b=10 km/hr

speed of the stream = 3km/hr

½ (a-b) = 3

½ (a-10) = 3  a-10=6  a=16 km/hr

speed of the boat in still water

= ½ (a+b)

= ½ (16+10)

= 26/2 = 13km/hr

7. A man can row 9 1/3 kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is

Ans:  4 2/3 km/hr

Basic Formula:

Speed of current = ½ (a-b) km/hr

Answer with Explanation:

Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr

Given:

Speed in still water = 9 1/3 = 28/3 km/hr

i.e, ½ (a+b) = 28/3 km/hr

 ½ (x+3x) = 28/3

 2x = 28/3  x = 28/ 2 x 3 = 14/3 km/hr

rate upstream b = 14/3 km/hr and

rate downstream a = 14/3 x 3 = 14 km/hr

speed of the current = ½ (a-b) = ½ (14 - 14/3)

= ½ (42-14/3) = 28/6 = 4 2/3 km/hr

8. A man can row a boat at 10kmph in still water. IF the speed of the stream is 6kmph, the time taken to row a distance of 80km down the stream is

Ans: 5hours

Basic Formula:

Speed of stream = ½ (a-b) km/hr

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Given:

Speed in still water, ½ (a+b) = 10 km/hr

 a+b = 20 km/hr ==(1)

speed of the stream, ½ (a-b) = 6km/hr

 a-b = 12 km/hr ==(2)

1+2  2a = 32

a = 16 km/hr

speed downstream =distance traveled / time taken

time taken = 80/16 = 5 hours

9. A boat takes 4hours for travelling downstream from point A to point B, and coming back to point  A upstream. If the velocity of the stream is 2km ph and the speed of the boat in still water is 4kmph, what is the distance between A and B?

Ans: 6km

Basic Formula:

Speed of stream = ½ (a-b) km/hr

Speed of still water = ½ (a+b) km/hr

Answer with Explanation:

Given:

Time taken by boat to travel upstream and downstream = 4 hours

Velocity of the stream, ½ (a-b) = 2km/hr

a-b = 4km/hr  1

velocity of the boat in still water = ½ (a+b) = 4km/hr

a+b = 8 km/hr  2

solving 1 x 2 we get a = 6 km/hr b = 2km/hr

let the distance between A and B be x km

x / 2 + x / 6 = 4  3x + x / 6 = 4  4x = 24 -- > x = 6

distance between A and B = 6km

10. IF a man rows at 6kmph is still water and 4:5kmph against the current, then his along the current is:

Ans:  7.5km/hr

Basic Formula:

Speed of the stream = ½ (a-b) km/hr

Speed in the still water = ½ (a+b) km/hr

Answer with Explanation:

Let the rate along the current i.e, speed upstream b

Speed downstream a

be x km/hr

a=4.5km/hr

== > ½ (a+b) = 6

 ½ (4.5 +x ) = 6

 4.5 + x = 12

 x = 12 – 4.5 = 7.5

speed along the current = 7.5 km/hr

11. If a man’s rate with the current is 11kmph and the rate of the current is 1.5kmph, then the man’s rate against the current is

Ans: 8km/hr

Basic Formula:

Speed of the stream = ½ (a-b) km/hr

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Given:

Rate downstream a = 11km/hr

Rate of current = ½ (a-b) = 1.5 km/hr

= a-b = 3km/hr

= 11-b = 3

= b= 8km/hr

rate against the current upstream = 8km/hr

12. Speed of a boat in standing water is 9kmph and the speed of the stream is 1:5kmph. A man rows to a place at a distance of 10.5 km and comes back to the starting point. The total time taken by him is

Ans:  24 hours

Basic Formula:

i. speed = distance traveled / time taken

ii. speed of the stream = ½ (a-b) km/hr

iii. speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed in still water= ½ (a+b) = 9km ph

= a+b = 18 --1

speed of the stream = ½ (a-b) = 1.5 kmph

= a-b = 3 kmph --2

solving 1 and 2 gives a = 10.5km/hr ; b=7.5 kmphr

Total time taken by him = 105/10.5 + 105/7.5 = 24 hours

13. A boat moves upstream at the rate of 1km in 10 minutes and downstream at the rate of 1km in 6 minutes. The speed of the current is

Ans: 2km/hr

Basic Formula:

Speed of the current = ½ (a-b) km/hr

Answer with Explanation:

Speed upstream ‘b’ = 1/10 x 60 km/hr

= 6 km/hr

speed downstream ‘a’ = 1/6 km/ min = 1/6 x 60

= 10km/hr

speed of the current = ½ (a-b)

= ½ (10-6)

= 2 km / hr

14. River is running at 2kmphr. If a man takes twice as long to row up as to row down the river. The rate of the man is still water is

Ans: 6km/hr

Basic Formula:

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Let the man’s rate upstream ‘b’ = x kmph.

Then his rate downstream ‘a’ = 2x kmph

Speed of the stream = 2 km/hr

= ½ (a-b) = 2

= a-b = 4

2x – x = 4

 x=4

a=8 ; b = 4

Speed in still water = ½ (8+4) = 6 km/hr

15. A man rows to a place 48km distant and back in 14 hours. He finds that he can row 4km with the stream in the same time as 3km against the stream. The rate of the stream is:

Ans: 1km/hr

Basic Formula:

Speed of the stream = ½ (a-b) km / hr

Speed = distance travelled / time taken

Answer with Explanation:

Suppose he moves 4km downstream in x hours

Then, downstream a= 4 / x km/hr

Speed upstream b = 3/ x km/hr

48 / 4 /x + 48 / 3/x = 14

x/4 + x/3 = 14/48 = ¼

3x + 4x / 12 = ¼  7x x 4 = 12  x = 3/7

a=28/3 km/hr b = 7km/hr

rate of stream = ½ (28/3 – 7 )

= 7/6 = 1.1 km/hr

16. The current of stream runs at 1kmph. A motor baot goes 35km upstream and back again to the starting point in 12hours. The speed of the motor boat in still water is

Ans:  6km/hr

Basic Formula:

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Let the speed of the motor boat in still water be x kmph then.

Speed downstream = x+1 km/hr

Speed upstream = x-1 km/hr

35/x+1 + 35/x-1 = 12

x-1+x+1/ (x+1) (x-1) = 12/35 == > 2x / x2 – 1 = 12/35

= 6x2 – 35 x – 6 = 0

= 6x2 – 36 x+x – 6 = 0

= 6x (x-6) + 1 (x-6) = 0  (6x+1) (x-6) = 0

x=6 km/hr

17. A boat covers 24km upstream and 36km downstream in 6 hours while it cover 35km upstream and 24km downstream in 6 ½ hours. The velocity of the current is

Ans:  2km/hr

Basic Formula:

Speed of the stream = ½ (a-b) km/hr

Answer with Explanation:

Let the rate upstream = x km / hr and

Rate downstream = y km/hr

24/x + 36/y = 6  36 x + 24y = 6 xy ...........1

36/x + 24/y = 6 ½  24x + 36y = 13/2 xy ............ 2

letting 1/x = a, 1/y = B

1+2  60 (1/x + 1/y) = 25/2  1/x +1/y = 5/24................ 3

2-1  12 (1/x – 1/y) = ½  1/x – 1/y = 1/24 .............. 4

3+4  x = 8 solving we get y=12

speed of stream = ½ (12-8) = 2km/hr

18. A man can row three quarters of a kilometre against the stream in 11 ¼ minutes and returns in 7 ½ minutes. The speed of the man is still water is

Ans: 5km/hr

Basic Formula:

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed upstream = 11¼ ×4/3, =  (45/4)×(4/3) = 15 min/km or 4 km/hr

Speed Downstream =  7½×4/3 = (15/2)×(4/3=  10 min or 6 km/hr

Let the speed of the man in still water be x kmph then.

x=½ (a+b) km/hr

x=½ (4+6)  or 5km/hr

19. The speed of a boat in still water is 15km/hr and the rate of current is 3 km/hr. the distance traveled downstream in 12 minutes is

Ans: 3.6km

Basic Formula:

Distance travelled downstream = speed downstream x time

Answer with Explanation:

Speed in still water = 15km/hr

½ (a+b) = 15km/hr

a+b = 30 km/hr -------------- (1)

Speed of current = 3 km/hr

½ (a-b) = 3km/hr

a-b= 6 km/hr ---------------(2)

(1)+(2)  2a = 36  a=18 km/hr

ie., speed downstream = 18 km/hr

Distance traveled downstream = 18 x 12/60 km = 3.6 km

20. A man can row 5kmph in still water. If the river is running at 1kmph, it makes him 75minutes to row to a place and back. How far is the place?

Ans: 3km

Basic Formula:

Speed of the stream = ½ (a-b) km/hr

Speed of the boat in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed in still water , ½ (a+b) = 5 == > a+b = 10 -- (1)

Speed of the stream , ½ (a-b) = 1  a-b = 2 --(2)

Solving 1 and 2 gives a=6 ; b=4

Let the required distance be x km

x/6 + x / 4 = 75/60 == > 10x/24 = 75/60

x = 24x 75/10x60 = 3

required distance = 3 km

21. If a man rows at the rate of 5kmph in still water and his rate against the current is 3.5kmph then the man’s rate along the current is

Ans:  6.5km/hr

Basic Formula:

Speed in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed in still water, ½ (a+b) = 5km/hr  a+b =10

Speed upstream b = 3.5 km/hr

Speed along the current i.e, downstream a = 10-3.5 = 6.5km/hr

22. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is :

Let the speed of the stream x mph. Then,

Speed downstream = (10 + x) mph,

Speed upstream = (10 - x) mph.

	36	-	36	=	90
	(10 - x)		(10 + x)		60

LCM = 100-x², since in Denominator is in the form (a+b)(a-b) = a2-b2. 36(10+x) – 36(10-x) = 90 100-x² 60 360+36x – 360-36x = 90 100-x² 60   Take 36 common, 36(10+x-10+x) = 90 100-x² 60 36(2x) = 3 100-x² 2 72x = 3 100-x² 2

72x ×2 = 3(100-x²)

144x = 300-3x²

3x²+144x-300 = 0.
x²+48x-100 = 0.
(x+50)(x - 2) = 0.
x = 2 mph.

Answer : 2

23. The rate of stream is 4 kmph. A boat goes 6 kms and back to the starting point in 2 hrs. The speed of the boat in still water?

Basic Formula:

Speed of the boat in still water = ½ (a+b) km/hr

Answer with Explanation:

Let he speed instill water = x km/hr

Speed of the stream = 4km/hr

Speed upstream = x- 4 k m/hr

Speed downstream = x+4 km/hr

6 / x-4 + 6/x+4 = 2

6(x+4 + x – 4) = 2(x2 – 16)

= 12x = 2x2 – 32

= x2 = 2x2 – 32

= x2 – 6x – 16 = 0

= (x-8) (x+2) = 0

= x= 8

speed in still water = 8 km/hr

Answer : 8 kmph

24. A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream:

Basic Formula:

Speed of the stream = ½ (a-b) km/hr

Answer with Explanation:

Let man’s rate upstream ‘b’= x kmph

Man’s rate downstream ‘a’ = 3x kmph

Speed of boat in still water = ½ (a+b) = 18 kmph

a+b = 36 kmph

3x +x = 36  x= 9 kmph

a= 27 km/hr ; b=9km/hr

speed of the stream = 1/2 (a-b)

= ½ (27-9)

= 9 km/hr

Answer ; 9 kmph

25. A man can row at 4.5 kmph in still water. It takes him twice as long to row up as to row down the river. What is the stream?

Basic Formula:

Rate of stream = ½ (a-b) km/hr

Answer with Explanation:

Let speed upstream = b= x km/hr

Speed downstream = a = 2x km/hr

Speed in still water = ½ (a+b) = 4.5

a+b = 9

2x + x = 9  x = 3

a=6km/hr ; b = 3km/hr

rate of stream = ½ (6-3) = 1.5 km/hr

Answer : 1.5 kmph

26. A boat running down stream covers a distance of 16 kms in 2 hrs, while for the same distance upstream, it takes 4 hours. The speed of the boat in still water:

Basic Formula:

Speed = distance traveled/ time taken

Speed of the boat in still water = ½ (a+b) km/hr

Answer with Explanation:

Speed downstream = 16/2 = 8km/hr

Speed upstream = 16/4 = 4km/hr

Speed of boat in still water = ½ (8+4) = 6km/hr

Speed of the boat in still water = 6km/hr

Answer : 6 km

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Question 11:NEXTGEN CAREER COACHING#9462900411--58-QA-

A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 km/hr, what is the speed of the boat in still water?
एक नाव, नीचे की ओर जाने में एक निश्चित दूरी 1 घंटे में पूरी करती है, की जबकि यह 1½ घंटे में वापस आती है। यदि धारा की गति 3 किमी / घंटा हो, तो स्थिर पानी में नाव की गति क्या है?
a. 12 km/hr
b. 13 km/hr
c. 14 km/hr
d. 15 km/hr  

Question 12:NEXTGEN CAREER COACHING#9462900411--58-QA-

A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
एक मोटरबोट, जिनकी गति स्थिर पानी में 15 किमी / घंटा है, 30 किलोमीटर नीचे की ओर चला जाता है और कुल 4 घंटे 30 मिनट के में वापस आता है। धारा (किमी / घंटा) की गति है:
a. 4
b. 5
c. 6
d. 10  

Question 13:NEXTGEN CAREER COACHING#9462900411--58-QA-

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 m/hr, the speed of the stream is:
एक नाव नीचे की ओर 36 मील की यात्रा करने में, अपस्ट्रीम यात्रा करने से, 90 मिनट कम समय लगाती है स्थिर पानी में नाव की गति 10 मीटर / घंटा है तो, धारा की गति है:
a. 2 m/hr
b. 2.5 m/hr
c. 3 m/hr
d. 4 m/hr  

Question 14:NEXTGEN CAREER COACHING#9462900411--58-QA-

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6½ hours. The velocity of the current is:
एक नाव 24 किमी अपस्ट्रीम और 36 किमी डाउनस्ट्रीम 6 घंटे में जबकि यह 36 किमी अपस्ट्रीम और 24 किमी डाउनस्ट्रीम 6½ घंटे चलती है। धारा का वेग है:
a. 1 km/hr
b. 1.5 km/hr
c. 2 km/hr
d. 2.5 km/hr  

Question 15:NEXTGEN CAREER COACHING#9462900411--58-QA-

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24 miles round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?
हमेशा की तरह अपनी नौकायन दर पर एक निश्चित नदी में, राहुल 12 मील की दूरी, नीचे की ओर जाने में ऊपर की ओर जाने की तुलना में 6 घंटे कम में पूरी करता हैं। अगर वह अपनी 24 मील आने जाने की दूरी अपनी हमेशा की नौकायन दर से दुगनी दर से पूरी सकता है, तो नीचे की ओर 12 मील की दूरी पूरी करने में ऊपर की ओर की 12 मील पूरी करने से 1 घंटा कम समय लगाता है। धारा की मील प्रति घंटा क्या है?
a. 31∕1
b. 21∕3
c. 32∕1.
d. 22∕3  

Question 16:NEXTGEN CAREER COACHING#9462900411--58-QA-

What is the speed of the boat in still water?
I. It takes 2 hours to cover the distance between A and B downstream.
II. It takes 4 hours to cover the distance between A and B upstream.
स्थिर पानी में नाव की गति क्या है?
ए और बी के बीच की डाउनस्ट्रीम दूरी को कवर करने मैं यह 2 घंटे लगते हैं ।
ए और बी के बीच अपस्ट्रीम दूरी को कवर करने मैं यह 4 घंटे लगते हैं
a. Only I is sufficient
b. Only II is sufficient
c. Both I & II are necessary to answer the question
d. Either I and II alone are sufficient.  

Question 17:NEXTGEN CAREER COACHING#9462900411--58-QA-

What is the speed of the boat in still water?
I. The boat covers a distance of 48 kms in 6 hours while running upstream.
II. The boat covers the same distance in 4 hours while running downstream.
स्थिर पानी में नाव की गति क्या है?
अपस्ट्रीम 48 किमी दूरी को कवर करने मैं यह 6 घंटे लगते हैं।
उसी दूरी को डाउनस्ट्रीम कवर करने मैं 6 घंटे लगते हैं.
a. Only I is sufficient
b. Only II is sufficient
c. Both I & II are necessary to answer the question
d. Either I and II alone are sufficient.  

Question 18:NEXTGEN CAREER COACHING#9462900411--58-QA-

A boat takes a total time of three hours to travel downstream from P to Q and upstream back from Q to P. What is the speed of the boat in still water?
I. The speed of the river current is 1 km/hr.
II. The distance between P and Q is 4 km.
एक नाव को नीचे की ओर P से Q व उपर की और Q से P स्थान की यात्रा में तीन घंटे का कुल समय लगता है. स्थिर पानी में नाव की गति क्या है?
I. नदी में धारा की गति 1 किमी प्रति घंटा है।
II. पी और क्यू के बीच की दूरी 4 किमी है।
a. Only I is sufficient
b. Only II is sufficient
c. Both I & II are necessary to answer the question
d. Either I and II alone are sufficient.  

Question 19:NEXTGEN CAREER COACHING#9462900411--58-QA-

What is the speed of stream?
I. The boat covers 24 km in 6 hours moving upstream.
II. The boat covers 24 km in 3 hours moving downstream.
III. The ratio between the speed of boat and stream is 3 : 1 respectively.
धारा की गति क्या है?
i. अपस्ट्रीम 24 किमी दूरी को कवर करने मैं नाव को 6 घंटे लगते हैं
ii. डाउनस्ट्रीम 24 किमी दूरी को कवर करने मैं नाव को 3 घंटे लगते हैं
III. नाव और धारा की गति के बीच का अनुपात क्रमश: 3 :1 है।
a. Any two of three
b. I and II only
c. II and III only
d. I and III only  

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