**Boats and Streams**

**Important facts: **

1)In water, the direction along the stream is called down stream.

2)Direction against the stream is called upstream.

3)The speed of boat in still water is U km/hr and the speed of

stream is V km/hr then

speed down stream =U + V km/hr

speed up stream = U – V km/hr

Formulae:

If the speed down stream is A km/hr and the speed up stream is

B km/hr then speed in still water = ½(A+B) km/hr

rate of stream =1/2(A-B) km/hr

**Problems:**

**1. In one hour a boat goes 11 km long the stream and 5 km
against the stream. The speed of the boat in still water is?**

Sol:

Speed in still water = ½ ( 11+5) km/hr= 8 kmph

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

Sol:

Let man’s rate up stream be xkmph

then, in still water =1/2[3x+x]=2x kmph

so, 2x= 18, x=9

rate upstream =9kmph

rate downstream =27 kmph

rate of stream = ½ [27-9]

= 9kmph

3.A man can row 71/2kmph in still water . if in a river running at 1.5 km an hour, if takes him 50 min to row to place and back. how far off is the place?

3.A man can row 71/2kmph in still water . if in a river running at 1.5 km an hour, if takes him 50 min to row to place and back. how far off is the place?

Sol: speed down stream =7.5+1.5=9kmph

speed upstream =7.5-1.5=6kmph

let the required distence x km. then ,

x/9+x/6=50/60 = 2x+3x= 5/6*18

5x=15, x=3

Hence, the required distence is 3 km

**4.A man can row 3 quarters of a km aganist the stream is
111/4 min. the speed of the man in still water is ?**

Sol: rate upstream = 750/625 m/sec =10/9 m/sec

rate downstream =750/450 m/sec = 5/3 m/sec

rate in still water =1/2[10/9+5/3] = 25/18 m/sec

= 25/18*18/5=5 kmph

**5.A boat can travel with a speed of 13 kmph in still water.
if the speed of stream is 4 kmph,find the time taken by the boat to go 68 km downstream?**

Sol: Speed down stream = 13+4= 17 kmph

time taken to travel 68km downstream =68/17 hrs

= 4 hrs

**6.A boat takes 90 min less to travel 36 miles downstream then
to travel the same distence upstream. if the speed of the boat in still water is 10 mph . The speed of the stream is :**

Sol: Let the speed of the stream be x mph .

then, speed downstream = [10+x]mph

speed upstream =[10-x] mph

36/[10+x] – 36/[10-x] = 90/60 =72x*60= 90[100-x2]

(x+50)(x-2) =0

x=2 kmph

7.At his usual rowing rate, Rahul 12 miles down stream in a certain river in 6 hrs less than it takes him to travel the same distence upstream. but if he could double his usual rowing rate for his 24 miles roundthe down stream 12 miles would then take only one hour less than the up stream 12 miles.what is the speed of the current in miles per hours?

7.At his usual rowing rate, Rahul 12 miles down stream in a certain river in 6 hrs less than it takes him to travel the same distence upstream. but if he could double his usual rowing rate for his 24 miles roundthe down stream 12 miles would then take only one hour less than the up stream 12 miles.what is the speed of the current in miles per hours?

Sol: Let the speed in still water be x mph and the speed of

the curren be y mph.

then, speed upstream = (x-y)

speed downstream =(x+y)

12/(x-y) – 12/(x+y) = 6

6(x2 – y2) m= 2xy => x2 – y2 =4y -(1)

and 12/(2x-y) – 12/(2x+y) =1 => 4×2 – y2 = 24y

x2= ( 24y + y2)/4 –>(2)

from 1 and 2 we have

4y+ y2 =( 24y+y2)/4

y=8/3 mph

y= 22/3 mph

**8.There is a road beside 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 kmph, while the other sails on a boat at a speed of 10 kmph . if the river flows at the speedof 4 kmph,which of the two friends will return to place A first ?**

Sol: Clearly, The cyclist moves both ways at a speed of 12 kmph

so, average speed of the cyclist = 12 kmph

the boat sailor moves downstream = (10+4) = 14 kmph

upstream =(10-4) = 6 kmph

So, average speed of the boat sailor =[ 2*14*6]/[14+6] kmph

=42/5 kmph =8.4 kmph

Since, the average speed of the cyclist is greater, he will

return to A first.

**9.A boat takes 19 hrs for travelling downstream from point A to
point B. and coming back to a point C midway between A and B.
if the velocity of the sream is 4 kmph. and the speed of the
boat in still water is 14 kmph. what is the distence between
A and B?**

Sol:

speed downstream =14+4 =18 kmph

speed upstream = 14 -4 = 10 kmph

let the distence between A and B be x km. then,

x/18 + (x/2)/10 = 19

x/18 + x/20 =19

19x/180 =19 =>x = 180km

Hence, the distence between A and B bw 180 km

bhargavanaiducomplete notes and short cut methods in boats and streams

SaahilQuestion 4 is completely wrong. Value of downstream is missing and in the solution u guys wrote 625 instead of 675