problems on boats and streams - vidyarthiplus.com

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

Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

If the speed downloadstream 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

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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 thenSpeed of the stream = ½ (a-b) kmph


Speed downstream a = 12kmphSpeed 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) wherea= speed downstreamb= speed upstream

Answer with Explanation:Speed downstream = distance travelled / time taken = 21/3

a = 7km / hrspeed upstream = 15/3 =5

b = 5km/hr

speed of the stream = ½ (a-b) km/hr= ½ (7-5)

= 1 km/hrspeed 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 /siii) a m/sec = a x 18/5 km/hr


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


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


Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hrGiven: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/hrSpeed 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 traveling 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/hrSpeed of still water = ½ (a+b) km/hr

Answer with Explanation:Given:Time taken by boat to travel upstream and downstream = 4 hoursVelocity 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/hrSpeed in the still water = ½ (a+b) km/hr

Answer with Explanation:Let the rate along the current i.e, speed upstream bSpeed downstream a

be x km/hra=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:8lm/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 takenii. speed of the stream = ½ (a-b) km/hriii. speed in still water = ½ (a+b) km/hr


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

= a+b = 18 --1speed of the stream = ½ (a-b) = 1.5 kmph

= a-b = 3 kmph --2solving 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. Aboat 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


Speed upstream ‘b’ = 1/10 x 60 km/hr

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

= 10km/hrspeed of the current = ½ (a-b)

= ½ (10-6)

= 2 km / hr




14. River is running at 2kmphr. IF takes a man twice as long to row ap 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


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=4a=8 ; b = 4speed 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 traveled / time taken

Answer with Explanation:Suppose he moves 4km downstream in x hours

Then, downstream a= 4 / x km/hrSpeed upstream b = 3/ x km/hr

48 / 4 /x + 48 / 3/x = 14x/4 + x/3 = 14/48 = ¼3x + 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:


Answer with Explanation:Let the speed of the motor boat in still water be x kmph then.

Speed downstream = x+1 km/hrSpeed 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 136/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 kilometer against the stream in 11 ¼ minutes and returns in 7 ¼ mintues. The speed of the man is still water is ans:5km/hr


Basic Formula:





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 traveled 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/hr½ (a-b) = 3km/hr

a-b= 6 km/hr --2

1+2 2a = 36 a=18 km/hrie., speed downstream = 18 km/hrdistance 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/hrSpeed 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=4Let 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:


Answer with Explanation:Speed in still water , ½ (a+b) = 5km/hr a+b =10Speed upstream b = 3.5 km/hrSpeed along the current i.e, downstream a = 10-3.5 = 6.5km/hr




22. There is road besides a river. Two friends started from a place A, moved to a temple

situated at another place B and then returned to A again. One of them moves on a cycle at

a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river

flows at the speed of 4 km/hr, which of the two friends will return to place A?

a. Both b. Boater c. Cyclist d. None of these


Basic Formula: Answer with Explanation:

The cyclist moves both ways at a speed of 12khr so average speed fo the cyclist – 12 km/hr

Also bat sailor moves downstream at 10+4 = 14km/hr and upstream 10-4 = 6km/hr

Average speed of the boat sailor = 2 x 14 x 6 / 14 +6 = 42/ 5 = 8.4km/hrThe average speed of cyclist is greater cyclist comes first and return to place A




23. A man can row 217 km/hr in still water. If in a river running at 1.5 km/hr, it takes

him 50 minutes to row to a place and back, how far off is the place?

a. 4 km b. 3 km c. 5 km d. 4.5 km


Basic Formula:

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

Answer with Explanation:Speed in still water, ½ (a+b) = 7 ½ km/hr == > a+b = 15 --(1)Speed of the stream , ½ (a-b) = 1.5 km/hr a-b =1.5 km/hr

a-b=3km/hr1+2 a=9 ; b = 6let the required distance be x kmx/9 + x/6 = 50/ 6015x/9 x 6 – 5/60 x = 9x 6 x 50/15x60 = 3kmrequired distance = 3km




24. 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


Basic Formula:


Answer with Explanation:Speed downstream a= 11/1 km/hrSpeed upstream b= 5/1 km/hrSpeed in still water = ½ (a+b) = ½ (11+5) = 8km/hr




25. A boat running downstream covers a distance of 16 km 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. 4 km/hr b. 6 km/hr c. 8 km/hr d. Data

inadequate


Basic Formula:Speed of boat in still water = ½ (a+b) km

Answer with Explanation:Speed downstream ‘a’ = 16/2 = 8km/hrSpeed upstream ‘b’ = 16/4 = 4k m/hrSpeed in still water = ½ (a+b) = ½ (8+4) = 6km/hr




26. A man row three-quarters of a kilometer against the stream in 4111 minutes. The

speed (in km/hr) of the man in still water is:

a. 4 b. 2 c. 3 d. 5


Basic Formula:

Rate in still water = ½ (a+b)km/hrii) a m/sec = a x 18/3 km/hr


Rate upstream = 750 / 675 m/sec = 10/9 m /secRate downstram = 750/450 m /sec = 5/3 m/ secRate in still water = ½ (10/9 + 5/3)

= 25/18 m /sec

= 25 / 18 x 18/5 km/hrrate in still water = 5 km/hr




27. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it

takes 4 hours to cover the same distance funning downstream. What is the ratio between

the speed of the boat and speed of the water current respectively?

a. 2 : 1 b. 3 : 2 c. 8 : 3 d. None of these


Basic Formula:

Speed of boat = ½ (a+b) km/hrSpeed of stream = ½ (a-b) km/hr

Answer with Explanation:Let the speed upstream be x km/hr and speed downstream be y km/ph.

Then

Distance covered upstream in 8 hours 48 minutes = distance covered downstream in 4 hours

x x 48 / 60 x 8 = y x 4 44x /5 = 4y y = 11/5 xratio between the speed of the boat and speed of the water current

½ (x+y) = ½ (y-x)

½ (x+11x / 5) = ½ (-x + 11x/5) 8/5 : 3/5 = 8:3




28. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream. a. 4 hours b. 3 hours c. 5 hours d. 2 hours


Basic Formula:

Speed upstream = speed in still water – speed of streamSpeed downstream = speed in still water + speed of stream

Answer with Explanation:Speed in still water = 13 km/hrSpeed of the stream = 4km/hrSpeed upstream m = 13 -4 = 9km/hrSpeed downstream = 13+4 = 19 km/hr

Time taken by the boat to go 68km downstream = 68 / 19 = 4 hours




29. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The

distance traveled downstream in 12 minutes is:

a. 1.2 km b. 1.8 km c. 2.4 km d. 3.6 km


Basic Formula:





30. A man can row at 5 km/hr in still water. If the velocity of current is 1 km/hr and it

takes him 1 hour to row to a place and come back, how far is the place?

a. 2.4 km b. 2.5 km c. 3 km d. 3.6 km


Basic Formula:Distance traveled = speed x time


Speed in still water = 5km/hrSpeed of the stream = 1 km/hrSpeed upstream = 5-1 = 4km/hrStream downstream = 5+1 = 6km/hr

Let the required distance be x kmx/4 + x/6 = 16x + 4x / 24 = 1

10x = 24 == > x= 24/10 = 2.4

required distance = 2.4 km




31. A man can row 319 km/hr 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:

a. 313 km/hr b.

913 km/hr c.

324 km/hr d.

214 km/hr


Basic Formula:

Speed of the current = ½ (a-b) km/hr

Answer with Explanation:Speed in still water = 9 1/3 km/hrLet man’s rate upstream = x km/hrMan’s rate downstream = 3x km/hr

Speed in still water = ½ (a+b) = 9 1/3 = 28/3

= ½ (x+3x) = 28/3

= 2x = 28/3 == > x = 14/3

speed upstream b= 14/3 speed downstream a=14

speed of current = ½ (a-b) = ½ (14-14/3) = 14/3 = 4 2/3 km/hr




32. A boat covers a certain distance downstream in 1 hour, while it comes back in 211

hours. If the speed of the stream be 3 km/hr, what is the speed of the boat in still water?

a. 12 km/hr b. 13 km/hr c. 14 km/hr d. 15 km/hr


Basic Formula:



Let the speed of the boat in still water be x kmphSpeed upstream = x-3 km/hrSpeed downstream = x+3 km/hr

(x+3)1 = (x-3) 1 ½2x +b = 3x – 9x = 15 km/hrspeed of the boat in still water is 15km/hr




33. 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:

a. 4 b. 5 c. 6 d. 10


Basic Formula:



Let the speed of the boat in still water be x kmph

speed in still water = 15km/hr

speed upstream = 15-x km/hr

speed downstream = 15+x km/hr

= 30 / 15+x + 30 / 15-x = 4 ½

= 30 (15-x) + 30 (15+x) / 152 – x2 = 9/2

= 900/152 – x2 = 9/2

= 152 – x2 = 900x2/9 = 200

= x2 = 225 – 200 = 25

= x= 5speed of the stream = 5km/hr




34. 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:

a. 2 m/hr b. 2.5 m/hr c. 3 m/hr d. 4 m/hr


Basic Formula:

Speed = distance traveled / time taken


Let the speed of the stream be x m/hrThenspeed downstream = 10+x m/hrSpeed upstream = 10-x m/hr

= 36/10+x + 36/10-x = 90/60

= 36/ 10+x + 36 / 10-x = 90/60

= 36(10-x) + 36(10+x) = 90/60 (102-x2)

= x2 + 48x +100 = 0= x+50) (x-2) = 0

= x= 2speed of the stream is 2km/hr




35. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36

km upstream and 24 km downstream in 216 hours. The velocity of the current is:

a. 1 km/hr b. 1.5 km/hr c. 2 km/hr d. 2.5 km/hr


Basic Formula:





36. A this 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?

a. 311 b.

321 c.

312 d.

322


Basic Formula:Speed of the current = ½ (a-b) km/hr

Answer with Explanation:Let the speed in still water be x m/hrSpeed of stream be y m/hrThen, speed upstream = x-y m/hr andSpeed downstream = x+y m/hr

12/x-y – 12 / x+y = 6 == > 6 (x2 – y2) = 24 y

x2 – y2 = 4y x2 = y2 + 4y2 -- 1

also12/ 2x-y - 12/2x +y = 1 4x2 – y2 = 24y

x2 = 24y + y2 / 4 --2

16y + 4y2 = 24y + y2

3y2 = 8 y y = 8/3

speed of the current = 8/3 m/hr = 2 2/3 m/hr




37. 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.

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.


Basic Formula:

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


Both speed upstream and speed downstream are needed. So answer is ( c )




38. 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.





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

Answer with Explanation:Both speed upstream and speed downstream are necessary so answer is ( c)




39. 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.





Basic Formula:

Answer with Explanation:Both I and II are necessary to answer the question




40. 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.

a. Any two of three b. I and II only c. II and III only

d. I and III only e. All I, II and III


Basic Formula:

Answer with Explanation:Any two of the condition is enough to find the speed of stream

Answer is a) any two of three




41. A boat takes 90 minutes less to travel 36 miles downstream thant o travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is : Answer : 2


Basic Formula:





42. 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?Answer : 8 kmph


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

Answer with Explanation:Let he speed instill water = x km/hrSpeed of the stream = 4km/hr

Speed upstream = x- 4 k m/hrSpeed 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




43. 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:Answer ; 9 kmph


Basic Formula:

Speed of the stream = ½ (a-b) km/hr


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




44. 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?Answer : 1.5 kmph


Basic Formula:

Rate of stream = ½ (a-b) km/hr


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




45. 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:Answer : 6 km


Basic Formula:

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


Speed downstream = 16/2 = 8km/hr

Speed upstream = 16/4 = 4km/hr

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

Speedofthe boat in still water = 6km/hr




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