The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to th

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08 May 2014 Time, speed and distance

The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.

OPtion

1) 2 km/hr
2) 3 km/hr
3) 4 km/hr
4) 5 km/hr
5) 6 km/hr
6) 7 km/hr
7) 8 km/hr
8) 9 km/hr
9) 10 km/hr
10)None of these

Solution

Solve
Speed of the boat in still water = 11 km/hr
Let the speed of stream = x km/hr
speed upstream = (11-x) km/hr
speed of downstream = (11+x) km/hr

According to the given condition
{12/(11+x)}+{12/(11-x)} = 11/4

Solve

Speed of the stream = 5 km/hr

Option 4)

Correct Option: 4 Best Solution (29)

Ann Theressa   10 years AGO

Let the speed of stream be x

Speed of boat in still water = 11
Speed of boat upstream = 11-x
Speed of boat downstream = 11+x

Distance = 12
Distance/speed = time

12/(11-x) + 12/(11+x) = 2 hours 45min
12*(22/(121-x^2) = 11/4
x^2 = 25
x = 5

Speed of stream = 5km/hr

Like? Yes (52) | No (21)  

susmit   10 years AGO

Let the speed of the stream be s km/hr.
Speed of boat in still water = 11km/hr
Speed of boat in upstream = (11- s) km/hr
Speed of boat in downstream = (11 + s)km/hr
Distance = 12km.
Therefore 12/(11-s)+12/(11+s) = 2(3/4)hr
12(11+s+11-s)/(11-s)(11+s) = 11/4
12*22/(121-s^2) = 11/4
12*2/(121-s^2) = ¼
Solving, s = 5
Speed of stream = 5km/hr
Hence option no.(4)

Like? Yes (35) | No (7)  

SAMPATH KUMAR   10 years AGO

The speed of boat in still water=11 km/hr distance=12 km
total time= 2 hrs 45 mins=11/4
let the speed of stream be x
and
the time taken by boat in still water be y
12/11=y
12/(11+x) + 12/(11-x)=11/4 (132-12x+12x+132)/121-x2 =11/4

264=1331-11x2/4
1056=1331-11x2 1
331-1056=11x2
275=11x2
25=x2
5=x
so the answer is 5km/hr

Like? Yes (11) | No (4)  

Devendra Marghade   10 years AGO

If the speed of the stream= x
12/(11+x) + 12/(11-x) = 11/4
On solving, 11x^2=275, x=5

Like? Yes (7) | No (3)  

Sanjeewani Indurkar   10 years AGO

let x be the speed of the stream.
upstream speed = (11-x) and downstream speed = (11+x)
Upstream Time=12/(11-x)[12kms is the distance]
Downstream Time=12/(11+x)
Total time =Upstream time + downstream time.

2hrs 45 mins =11/4 hours.
11/4=12/(11-x)+12/(11+x)

After solving x= +5 or -5. Speed is scalar qty therefore answer is 5.

Like? Yes (7) | No (4)  

DILEEP KUMAR   10 years AGO

let x km/hr be the speed of the stream
distance= 12km
time taken to upstream= 12/(11-x)
time taken to downstream = 12/ (11+x)
total time = 2hr 45 min = 11/ 4 hrs
so
(12/(11-x))+(12/(11+x))= 11/4
=> x= 5
i.e speed of the stream is 5 km/hr

Like? Yes (6) | No (3)  

MD SOHAIL AKHTER   10 years AGO

let the speed of stream be x km/hr
A/Q
12/(11+x)+12/(11-x)=11/4
on solving we get x= 5km/hr

Like? Yes (6) | No (4)  

RAKESH   10 years AGO

12[1/(11+x) + 1/(11-x)] = 2 3/4 = 11/4

=> x=5

Like? Yes (5) | No (3)  

PAWAN KUMAR   10 years AGO

[12/(11-x) + 12/(11+x)]=2.75
=>x=5 km/hr

Like? Yes (4) | No (2)  

Dada Khalandar   10 years AGO

t x=speed of stream
11+x=speed of boat downstream
11-x=speed of boat upstream
2 hr and 45 min=2.75 hr
Travel time=distance/speed
**


12/(11+x)+12/(11-x)=2.75
LCD:(11+x)(11-x)
12(11-x)+12(11+x)=2.75(11+x)(11-x)=2.75(121-x^2)=332.75-2.75x^2
132-12x+132+12x=332.75-2.75x^2
264=332.75-2.75x^2
2.75x^2=332.75-264=68.75
x^2=68.75/2.75=25
x=5
speed of stream= 5 km/hr

Like? Yes (4) | No (2)  

sushmita pattanaik   10 years AGO

Speed of boat in still water=x
Speed of stream=y
Total time taken= (12/(x+y))+(12/(x-y)) = 2+3/4 hrs
Solve for y

Like? Yes (7) | No (6)  

Bhagyashree Bhatt   10 years AGO

Let the speed of the stream be x km/hr.
Speed of boat in still water = 11km/hr
Speed of boat in upstream = (11- x) km/hr
Speed of boat in downstream = (11 + x)km/hr
Distance = 12km.
A.T.Q 12/11-x+12/11+x = 2(3/4)hr
12(11+x+11-x)/(11-x)(11+x) = 11/4
12x22/121-x2 = 11/4
12x2/121- x2 = ¼
121- x2 = 96
X = sqrt.(25) = 5
Speed of stream = 5km/hr.

Like? Yes (4) | No (3)  

Lavanya   10 years AGO

let distance=x
let speed of boat in still water=v1
let speed of stream=v2
as speed=distance/time
total time taken for journey=t=x/(v1+v2)+x/(v1-v2)
given x=12km
v1=11km/hr
t=2hours 45min=2+45/60 hours=11/4 hours
therefore 12/(11+v2)+12/(11-v2)=11/4
so, v2=5km/hr

Like? Yes (4) | No (4)  

DINESH KUMAR   10 years AGO

Let the speed of the stream be x km/hr.
Speed of boat in still water = 11km/hr
Speed of boat in upstream = (11- x) km/hr
Speed of boat in downstream = (11 + x)km/hr
Distance = 12km.
A.T.Q 12/11-x+12/11+x = 2(3/4)hr
12(11+x+11-x)/(11-x)(11+x) = 11/4
12x22/121-x2 = 11/4
12x2/121- x2 = ¼
121- x2 = 96
X = sqrt.(25) = 5
Speed of stream = 5km/hr.

Like? Yes (3) | No (3)  

AMIT   10 years AGO

let speed of stream =x km/hr
12/(11+x)+12/(11-x)=2*45/60
after solving we will get x=5

Like? Yes (4) | No (4)  

C.Aarthi   10 years AGO

speed in stream =x
Speed in still water =11
upsteam speed=11+x
downstream spead=11-x
todal distance =12
And time =165/60

(12/11+x) + (12/11-x) = 165/60
ans :x=5

Like? Yes (3) | No (3)  

Barun kumar singh   10 years AGO

> let speed of stream=x
> upstream=11-x , downstream=11+x
> time =distance /speed
> 12/(11+x)+12/(11-x)=2+(45/60)
> 12(11-x)+12(11+x)=2.75(11+x)(11-x)
> 132-12x+132+12x =2.75(121-x^2)
=332.75-2.75x^2
> 264=332.75-2.75x^2
> 2.75x^2=332.75-264
> x^2=68.75/2.75
=25
Ans x=5 km/hr

Like? Yes (2) | No (3)  

Udhaya kumar   10 years AGO

let x as speed of stream
(12/(11-x))+(12/(11+x))= 2.75....
by solving this we get x = 5.........

Like? Yes (3) | No (4)  

SONU GUPTA   10 years AGO

12/(11+x)+12/(11-x)=2.75
LCD:(11+x)(11-x)
12(11-x)+12(11+x)=2.75(11+x)(11-x)=2.75(121-x^2)=332.75-2.75x^2
132-12x+132+12x=332.75-2.75x^2
264=332.75-2.75x^2
2.75x^2=332.75-264=68.75
x^2=68.75/2.75=25
x=5
speed of stream= 5 km/hr

Like? Yes (2) | No (3)  

Gitanjali K   10 years AGO

let speed of stream=x
speed of boat downstream=11+x
speed of boat upstream=11-x

2 hr 45 min=2.75 hr

time=distance/speed

12/(11-x)+12/(11+x)=2.75
12[1/(11-x)+1/(11+x)]=2.75
12[22/121-x^2]=2.75
22/121-x^2=2.75/12
22*12/2.75=121-x^2
96=121-x^2
x^2=25
x=5
therefore,speed of stream = 5 km/hr

Like? Yes (4) | No (5)  

ravi prakash   10 years AGO

121-96=stream2
stream=5km/hr

Like? Yes (3) | No (4)  

murari kumar   10 years AGO

Let speed of stream.is=x
Therefore
{12÷(11+x)}+{12÷(11-x)}=2*(45÷60)
After solving this equation
X=5km/hr

Like? Yes (3) | No (4)  

chandan jha   10 years AGO

12/(11-x)+12/(11-x)=11/4;
x=5;

Like? Yes (3) | No (4)  

NAGENDRA P   10 years AGO

Let x=Speed of stream
11+x=Speed of boat downstream
11-x=Speed of boat upstream
travel time=2.75hour
travel time=Distance/Speed
12/(11+x)+12/(11-x)=2.75
x=5km/hr
So option(4)

Like? Yes (3) | No (4)  

harshal agrawal   10 years AGO

12/(11+x) + 12/(11-x) = 11/4

Like? Yes (2) | No (3)  

Harivignesh.B   10 years AGO

let x=speed of stream
11+x=speed of boat downstream
11-x=speed of boat upstream
2 hr and 45 min=2.75 hr
Travel time=distance/speed

12/(11+x)+12/(11-x)=2.75
LCD:(11+x)(11-x)
12(11-x)+12(11+x)=2.75(11+x)(11-x)=2.75(121-x^2)=332.75-2.75x^2
132-12x+132+12x=332.75-2.75x^2
264=332.75-2.75x^2
2.75x^2=332.75-264=68.75
x^2=68.75/2.75=25
x=5
speed of stream= 5 km/hr

Like? Yes (2) | No (3)  

indrajeet yadav   10 years AGO

let speed of stream=x kmph
12/11-x+12/11+x=11/4
on solving this equation
x=5 kmph

Like? Yes (2) | No (3)  

vicky kumar   10 years AGO

Let the speed of the stream be x km/hr.
Speed of boat in still water = 11km/hr
Speed of boat in upstream = (11- x) km/hr
Speed of boat in downstream = (11 + x)km/hr
Distance = 12km.
A.T.Q 12/(11-x)+12/(11+x) = 2(3/4)hr
12(11+x+11-x)/(11-x)(11+x) = 11/4
12*22/(121-x^2)=11/4
BY solving above
x=5

Like? Yes (2) | No (4)  

rajani   10 years AGO

the total time taken to complete the journey=2hrs45mins
time=distance/speed
i.e,11/4=(12/11-x)+(12/11+x),
on solving this we get x=5,
that is speed of stream=5km/hr

Like? Yes (3) | No (5)