19 boats and streams

8/2/2019 19 Boats and Streams

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~--------UPS~ROWINGDOWNSTREAMROWING

I_I

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19.1 INTRODUCTIONThe following terms are frequently used in the- problems on boats and streams:(a) Still Water: It implies that the speed of water in the river is zero.(b) Stream Water: It implies that the water in the river is moving.

19.\PEED OF MAN (BOAT) AND STRFAMDirection----------,~

Man's rate of rowing (or speed of boat) in still water =x kmIh .

Speed of current (or stream) = y kmIh .Direction

Let, the man's rate of rowing (or speed of boat) in still water = x kmIhand the speed of stream (or current) = y km/h(a) Downstream (With the stream) Rowing:

I t indicates that the stream favours the man's rowing (or boating).i.e. direction of rowing and direction of flow (stream) is same.:. Man's rate of rowing downstream = DOWNSTREAM RATE = x + Y

(b) Upstream (Against the stream) Rowing:Itindicates that the stream flows against the man's rowing (or boating)i.e. direction of rowing and direction of stream (current) are opposite.:. Man's rate of rowing upstream = UPSTREAM RATE = x - y

19.3 IMPORTANT FORMUlAEAssumption:Man's rate of rowing in still water = xSpeed of stream (current) = y


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19-2 Quantitative Aptitude for Competitive Examinations

downstream distancetime to cover it [ t

distance]:. ra e:;:: - = - = ~ = - = - = -time1. Downstream Rate :;::x + y :;::

:;::

upstream distancetime to cover it [ t distance]:. ra e :;::::;:..:..=.::.c...:..time2. Upstream Rate = x - y

=

3. Man's rate in STILL water = x = 1 [DOWNSTREAM rate +UPSTREAM rate]21= 2 since x = _ ! _ [(x + y) + (x - y) ]2

= 1 [DOWNSTREAM rate - UPSTREAM rate]21 [ddown ; 1 .= ' 2 tdown - tup smce y =

5. ~en downstream distance:;:: upstream distance, then

4. Speed of stream = y

~ [(x + y) - (x - y) ]

=Man's rate in still waterSpeed of stream6. When downstream distance = upstream distance, thenAverage speed for total journey (UP + DOWN)

Upstream rate x Downstream rate= Man's rate in still water7. When downstream distance = Upstream distance, then

Man's rate in still water x Total distance *Total Journey time (tup + tdown ) = Upstream rate x Downstream rate* Total distance = downstream distance + upstream distance

= 2 x anyone side distance [Since downstream distance = upstream distance]Solved Ex.mpl

E-1 A man can swim downstream at 8 kmJh and upstream at 2 kmIh . Find man's rate _instill water andthe speed of current.

5-1 Man's rate in still water e 2 [Up + Down] [Refer formula (3)J

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1 [ d d D dUp]S-2 Speed of current y = - - - -2 tdo tup {Refer formula (4)J

Boats and Streams 19-3

= 1 (8 + 2) = 5 k:mIh21Speed of current = 2 [Downstream - Upstream rate] [Refer formula (4)J1

= (8 - 2) = 3 kmIh.2E-2 A man rows upstream 20 km and downstream 30 km taking 5 hours each. Find the speed of current.

E-3= ~ [ 3 5 - 2 5 J = 1 kmIh.

A boat man can row 2 km against the stream in 20 min. and return in 15 min. Find the rate of rowingin still water and the speed of current.Here distance is fixed, therefore, ddu = dup = d,Using the formula (3), we get

S-3

x (Man's speed of rowing in Still water) = ! ! : _ [ _ l _ + _ 1 _ ]2 tdn tup {Refer formula (3)J

d [ 1 1 ](Speed of current ) = - - - -2 tdu tup {Refer formula (4)J

= % [ ; 0 - 115J = ~ kmlmin = 1 kmIh.E-4 A man can row 4 km/h in still water and he finds that it takes him twice as long to row up as to row

down the river. Find the rate of stream.S-4 Using the formula (5),

speed of streamtd u + tuptup - td u

tup = 2 X tdu

Man's rate in still water

Since4- - - - ~ - - - - - = =speed of stream - tdn + 2 tdn 1

3

4speed of stream = - kmIh = 1.3 kmIh.3

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Quantitative Aptitude for Competitive ExaminationsA man can row 6 kmIh in the still water. If the river is running at 2 kmIh, it takes him 3 hours torow to a place and back. How far is the place?

5 Using the formula, tdown + ~p = total time,_d_ + _d_ = total time ~ ! ! : . . + ! ! : . . . = 3 . . d = 8 km,x+y x-y 8 4

6 The speed of a boat in still water is 15 kmIh and the rate of current is l3 kmIh. Find the distancetravelled downstream in 15 min.Distance in downstream ;::::downstream rate x time

= (15 + l3) x ~ = 7 km.~ 60A man can row at a speed of 4.5 kmIh in still water to a certain upstream point and back to the startingpoint in a river which flows at 1.5 kmIh. Find his average speed for total journey.

7 x = 4.5 kmIh (given) and y = 1.5 kmIhUsing the formula (6),

Upstream rate x Downstream rateAverage speed for total journey = Speed in still water(x+y)x(x-y) 6x3= = = 4 km/h.x 4.5

A man rows 10 km upstream and back again to the starting point in 55 min. If the speed of streamis 2 kmIh, find the speed of rowing in still water.Let speed of rowing in still water = xalso, y = speed of stream = 2, total time T = ~ hHence, using the formula (7), we get

Speed in still water x Total distanceTotalthne= ~-----------------------upstream rate x downstream rate

~ 55 x x 2 x 1060 (x+2)(x-2)

55 (x2 _ 22) = 2 x x x 10 ~60~ (x - 22) (I lx + 2) = 0 ..

l l x 2 - 240x - 44= 0x = 22, Since (- )ve value of x is not admissible.

A motor boat can travel at 10 kmIh in still water. It travelled 91 km downstream in a river and thenreturned, taking altogether 20 hours. Find the rate of flow of river.

9 Motor boat speed in still water (x) = 10 kmIhLet, the rate of flow of river = y, then,Total journey time T = 20 h is givenHence, using the formula (7), we get

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Boats and Streams 19-5Speed in still water x Total distanceTotal time = ------------upstream rate x downstream ratelOx2x91

20= ------(1O+y)(10-y)91 x 20 = 20 ( 102 - 1) ~ 1-02 + 91 = 019 i.e., y = 3 kmIh :. Flow of river = 3 kmIh.

I RE GUL AR P RO BL EM S I(1) A person can swirtliiiStilIWater at 4 kmIh. If the speed of water is 2 km/h, how many hours will

the man take to swim back against the current for 6 km. (UTI, '90)(a) 3 (b) 4 1(c) 4-

2I (d) Insufficient data (e) None of these~2) A boat goes 100 km downstream in 10 hours, and 75 km upstream in 15 hours. The speed of the

stream is(a) 7 kmIh (b) 5 kmIh (c) 3 kmIh (d) 2 _ ! _ kmIh (e) None of these2

(3) A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rateis(a) 1 kmIh (b) 5 kmIh (c) 8 km/h (d) 6 kmIh (e) Data insufficient

(4) A man can swim in still water at 4.5 kmIh, but takes twice as long to swim upstream than downstream.The speed of the stream is(a) 3 (b) 7.5 (c) 2.25 (d) 1.5 (e) 6

(5) If a man takes 3 hours to row 3 km upstream or 15 km downstream, then the speed of the currentis(a) 4 (b) 9 (c) 2 (d) 6 (e) Data insufficient

(6) A man can row in still water at 7 kmIh and the rate of stream is 3.5 kmIh. A distance of 10.5 kmin going upstream is covered in(a) 1.5 h (b) 1 h (c) 3 h (d) 15 h (e) 10 h

(7) A boat goes downstream at U mls and upstream at V mls. Then the speed of the boat in still wateris

1(a) - (U - V)2' (b) U - V (c) _ !_ (U + V)2(d) U + V (e) 2 UV

(8) A boat goes downstream at the rate of U mls and upstream at V mls. Then the speed of the streamIS

(a) t (U - V)(d) U + V

(b) U - V (c) ~ (U + V)(e) 2 UV

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2 2 2xd(a) (x- - y ) = -T

(b) (x + y) = dTx -y

(c) xy = dT

9-6 Quantitative Aptitude for Competitive Examinations91 A man rows d km upstream and back again downstream to the same point in T hours. The speed ofrowing in still water is x kmIh and the rate of stream is y kmIh, then

(d) x2 +i 2 xdT (e) Data insufficientThe speed of a boat in still water is 15 kmIh and the rate of stream is 5 kmIh. The distance travelleddownstream in 24 min. is(a) 4 km (b) 8 krn (c) 6 km (d) 16 km (e) None of theseIf the speed of boat in still water, stream rate and time of travel are kept constant, and distance indownstream = ddn and distance tra~pstream = dup, then

I (a) ddn = d u p,d) ddn + dup = 1 (e) ddn x d u p = constantU A man rows 40 krn upstream in 8 hours and a distance of 36 krn downstream in 6 hours, then speedof stream is(a) 0.5 kmIh (b) 5.5 kmIh (c) 6 krn/h (d) 5 krn/h

13 A man rows 40 krn upstream in 8 hours and a distance of 36 krn downstream in 6 hours, then thepeed of man in still water is(a) 0.5 kmIh (b) 5.5 kmIh (c) 6 km/h (d) 5 krn/h (e) None of these

14 Ifa man's downstream rate is 10 krn/h, and the rate of stream is 1.5 km/h, then the man's upstreamrate is(a) 13 kmIh (b) 10 km/h (c) 3 krn/h (d) 7 krn/h (e) Data insufficient

C' Ifa man rows at 8 km/h in still water and his upstream rate is 5 krn/h, then the man's rate along thecurrent (downstream) is(a) 21 krn/h (b) 8 krn/h (c) 16 krn/h (d) 11 krn/h (e) 10 krn/h

16) The rowing speed of man in still water is 20 krn/h. Going downstream, he moves at the rate of 25 km/h. The rate of stream is(a) 45 km/h (b) 2.5 krn/h (c) 12.5 kmIh (d) 5 krn/h (e) 10 kmIhHint: Downstream Rate = (Speed in still water + Speed of stream).

1 Ifa man goes upstream at 6 km/h and the rate of stream is 2 km/h, then the man's speed in still wateris(a) 4 km/h (b) 8 km/h (c) 2 km/h (d) 12 krnJh (e) 3 km/hHint: Upstream rate = (Speed in still water - Speed of stream).

1 A boat goes 12 krn upstream in 48 min. The speed of stream is 2 km/h. The speed of boat in stillwater isa) 13 km/h (b) 2.25 km/h (c) 17 kmIh (d) 15 km/h (e) Data insufficienters

1. (a)1.

2 . ( d )11. (c)

3. (b)12. (a)

4 . ( d )13. (b)

5. (c)14. (d)

6. (c)15. Cd)

7. (c)16. (d)

8 . (a)17. (b)

9. (a)18. (c)

19 boats and streams

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