MTS / POSTMAN / GDS TO PA / PA RECRUITMENT MATERIAL

MTS / POSTMAN / GDS TO PA / PA RECRUITMENT MATERIAL

                                       BOATS AND STREAMS

1.When a boat is moving in the same direction as the stream or water current, the boat is said to be moving with the stream or moving downstream.

2.Instead of boats in water, it could be a swimmer or a cyclist cycling against or along the wind.

3. When a boat is moving in a direction opposite to that of the stream or water current, the boat is said to be moving against the stream or water current or moving downstream.

4. When the speed of the boat is given, it is the speed of the boat in still water.

5. Speed of the boat against stream or while moving upstream = Speed of the boat in still water - Speed of the stream.

6. Speed of the boat with stream or while moving downstream= Speed of the boat in still water + Speed of the Stream.

7. If 'p' is the speed of the boat down the stream and 'q' is the speed of the boat up the stream, then,

Speed of the boat in still water = (p+q) / 2.

Speed of the boat of the water stream = (p-q) / 2.

8.These problems are governed by the following results:

Downstream (along the current) speed (D) = Boat speed (B) + current (stream) speed (C).         D=B+C

Upstream (against the current) speed (U) = Boat speed – current (stream) speed. U=B–C

Speed of the boat = average of downstream and upstream speeds B = (D + U)/2

Speed of the current = half the difference of downstream and upstream speeds    C = (D – U)/2

                                             Example:

1.A boat takes 5 hours to go from A to B and 8 hours to return to A. If AB distance is 40 km, find the speed of (a) the boat and (b) the current.

Sol: Since B to A takes more time, it is upstream and hence AB is downstream. Downstream speed = 40/5 = 8 kmph.

Upstream speed= 40/8 = 5 kmph.

Boat speed = (8 + 5)/2 = 6.5 kmph.

Current speed = (8 – 5)/2 = 1.5 kmph.

2.A man cn row a boat at 20 kmph in still water.If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream ?

Sol: Speed of downstream = boat speed + stream speed = 20 + 6 = 26 kmph

Time required to cover 60 km downstream = d/s = 60/26 = (30/13) hours.

3.The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream ?

Sol: The time taken to row his boat upstream is twice the time taken by him to row the same distance downstream. Therefore, the ratio of the time taken is (2:1). So, the ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3:1 .Thus, Speed of the stream = (42)/3 = 14 kmph.

4. A boat travels 36 km upstream in 9 hours and 42 km downstream in 7 hours. Find the speed of the boat in still water and the speed of the water current ?

Sol:  Upstream speed of the boat = 36/9 = 4 kmph

Downstream speed of the boat = 42/ 7 = 6kmph.

Speed of the boat in still water = (6+4) / 2.

= 5 kmph

Speed of the water current = (6-4) /2

= 1 kmph

5.A man can row at 10 kmph in still water. If it takes a total of 5 hours for him to go to a place 24 km away and return, then find the speed of the water current ?

Sol:  Let the speed of the water current be y kmph.

Upstream speed = (10- y) kmph

Downstream speed = (10+y) kmph

Total time = (24/ 10+y) + ( 24/10-y) = 5

Hence, 480/ (100-y2 ) = 5

480= 500-5y2, 5y2= 20

y2= 4, y = 2 kmph.

6.A man can row x kmph in still waters. If in a stream which is flowing at y kmph, it takes him z hrs to row from A to B and back (to a place and back), then

Sol: The distance between A and B = z ( x2 - y2) / 2x.

7. A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. How far is the place?

Sol:  Required distance = 1 x ( 62 - ( 1.2)2) kmph

= (36 - 1.44) / 12

= 2.88 km.

In the above case, If distance between A and B, time taken by the boat to go upstream and back again to the starting point, speed of the stream are given; then the speed of the boat in still waters can be obtained using the above given formula.

8. A man rows a certain distance downstream in x hours and returns the same distance in y hrs. If the stream flows at the rate of z kmph then,

Sol: The speed of the man in still water = z(x+y) / ( y-x) kmph.

9.Ramesh can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 kmph. Find the speed of Ramesh in still water?

Sol:  Ramesh's speed in still water = 3 (9+6) / (9-6)

= 15 kmph.

10.A man rows a certain distance downstream in x hours and returns the same distance in y hours. If the speed of the man in still water z kmph, then

Sol: Speed of the stream = z (y-x) / (x+y) kmph.

11. Abhinay can row a certain distance downstream in x hours and returns the same distance in y hours. If the speed ofAbhinay in still water is 12 kmph. Find the speed of the stream?

Sol: Speed of the stream = 12 ( 9-6) / (9+6)

= 2.4 kmph.

12. If a man can swim downstream at 6 kmph and upstream at 2 kmph, his speed in still water is 

Speed in still water = (1/2) * (6 + 2) km/hr = 4 km/hr

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

Sol: Rate upstream = (7/42)*60 kmh = 10 kmph. Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x-3 = 10 or x = 13 kmph.

14. A man rows 13 km upstream in 5 hours and also 28 km downstream in 5 hours. The velpciy of the stream is   

Sol: speed upstream = (13/5) kmph
speed downstream (28/5) kmph
Velocity of stream = (1/2)[(28/5) - (13/5)] = 1.5 kmph

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

Sol; Speed downstream (10+6) km/hr 16 km/hr.
Time taken to cover 80 km downstream = (80/16) hrs = 5 hrs

16.A man can row 9 and 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

Sol: Let speed upstream is x kmph. Then, speed downstream = 3x kmph. Speed in still water = (1/2)(3x + x) kmph = 2x kmph. 2x = 28/3 x = 14/3 Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr. speed of the current = (1/2)[14 - (14/3)] = 14/3 = 4 and 2/3 kmph

17.A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is

Sol: Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec.
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec. = 25/18 m/sec
= (25/18)*(18/5) kmPh = 5 kmph

18.If anshul rows 15 km upstream and 21 km downstream taking 3 hours each time, th’en the speed of the stream is : .

Sol: Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph.

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

Sol: Suppose he move 4 km downstream in x hours. Then,

Speed downstream =		4		km/hr.
		x

Speed upstream =		3		km/hr.
		x

	48	+	48	= 14 or x =	1	.
	(4/x)		(3/x)		2

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream =	1	(8 - 6) km/hr = 1 km/hr.
	2

20. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

Sol: Let man's rate upstream be x kmph.

Then, his rate downstream = 2x kmph.

(Speed in still water) : (Speed of stream) =		2x + x		:		2x - x
		2				2

=	3x	:	x
	2		2

   = 3 : 1.