Aptitude - Boats and Streams - Discussion

12. 

A man can row three-quarters of a kilometre against the stream in 11 minutes and down the stream in 7 minutes. The speed (in km/hr) of the man in still water is:

[A]. 2
[B]. 3
[C]. 4
[D]. 5

Answer: Option D

Explanation:

We can write three-quarters of a kilometre as 750 metres,

and 11 minutes as 675 seconds.

Rate upstream = 750 m/sec = 10 m/sec.
675 9

Rate downstream = 750 m/sec = 5 m/sec.
450 3

Rate in still water = 1 10 + 5 m/sec
2 9 3

   = 25 m/sec
18

   = 25 x 18 km/hr
18 5

   = 5 km/hr.


Gulam said: (Jun 21, 2010)  
how to find it minutes to millisecond
plz reply me
Thanks

Mohan said: (Dec 25, 2010)  
How can we find the value for Rate Upstream and Rate downstream
reply plz /....

Sumathipriya said: (Jan 7, 2011)  
how to find rate upstream and rate downstream?

Nagarjun said: (Jan 11, 2011)  
rate of upstream is equal to speed of boat in upstream..say->A
(and)
rate of downstream is equal to speed of boat in downstream..->B

speed of boat in still water = 1/2(A+B)...say->X

speed of stream or rate of stream = 1/2(A-B)...say->Y

then speed of boat in downstream = X+Y
speed of boat in upstream = X-Y

Jerry said: (Jun 28, 2011)  
3/4=0.75km
0.75*1000=750km

Sanchit said: (Nov 6, 2011)  
Distance=3/4km
time taken upstream=11 1/4 min= 45/4min
time taken upstream (in hours)=45/48*1/60=3/16 hrs
speed upstream = distance (km)/time (in hours)
=3/4 * 16/3= 4kmph
time taken downstream = 7 1/2 = 15/2 min
time taken downstream (in hrs) = 15/2*1/60=1/8 hrs
speed downstream = distance/time = 3/4*8 = 6 kmph
now, speed in still water = 1/2* (4+6)
= 10/2
= 5 kmph
Isn't it easier ?

Santhosh said: (Nov 22, 2011)  
@sanchit : You Have done Perfect :)

Deepi said: (Feb 5, 2012)  
Rate of upstream and rate of downstream means speed of upstream and speed of downstream
From the formula Distance=time*speed
rate of upstream=Distance/time

Here they given as three quarters of km that is 3/4 and minutes from that we can find the speed in m/sec.

So totally solution comes in the form of m/sec to covert the m/sec in km/h we need to multiply 18/5.

Deepi said: (Feb 5, 2012)  
To convert mints to seconds just multiply by 60.
to convert mints to hour just divide by 60.
here 11 1/4 mint (11*4+1) 45/4
To convert 45/4*60=675

Nizampatnam said: (Oct 12, 2012)  
Yes Down Stream 7 1/2=15/2*60
=900/2
=450sec

Jyoti said: (Jul 27, 2013)  
How does 3 quarters of kilometers is converted?

Manish said: (Jul 27, 2013)  
How did you evaluate 7*(1/2) ?

Kishor said: (Aug 5, 2013)  
Downstream : Upstream
...................................................
Distance(D) 3/4 x 1 km : 3/4 x 1 km

Time(T) 15/2 x 60 hr : 45/4 x60 hr


Speed(D/T) (3/4 x1)/(15/2 x60)=6 : (3/4 x1)/(45/4 x60)=4


Speed of man in still water = (6+4)/2 = 5 km/hr.

Fahmi said: (Dec 28, 2013)  
We can do it more easy way.

(3/4) * (4/45) *60 = 4 km.

(3/4) * (2/15) *60 = 6 km.

1/2 (4+6) km = 5 km.

Neelam said: (Apr 1, 2014)  
How we find downstream time as it is not mention in the question?

Sunil said: (Apr 13, 2014)  
How did you find rate of downstream ?

Bijendra Singh said: (Jul 24, 2014)  
Downstream time is given there 7 1/2 so it is 15/2*60.

i.e. 900/2 = 450

Nikul Rana said: (Nov 1, 2015)  
Let we assume the speed of man in still water = X kmph;

And the speed of water current = Y kmph;

So, The speed downstream = X+Y;

And the speed against the stream = X-Y;

Therefor we can say that X-Y = (3/4)/(45/4) = 4;

X-Y = 4.....(1);

And X+Y = (3/4)/(15/2) = 6;

X+Y = 6.....(2);

So that we get X = 5; //The speed of the man in still water.

Buny said: (Jan 1, 2016)  
How to find time of download stream? How it is calculated 15/2?

Sudarshan said: (Jan 23, 2016)  
Man Speed = 1/2 (Upstream Speed + Downstream Speed).

= 1/2 (750*4/45*60 + 750*2/15*60).

= (1/2)*(750/60)(2/15)( 2/3 + 1).

= (750*2/2*60*15) * (5/3).

= 25/18 meters/sec.

= (25/18)*(18/5) Km/hr.

= 5 Km/hr.

Dhakshina said: (Jan 26, 2016)  
Let us consider distance as 3/4 km.

Upstream speed is 45/4.

Speed travelled is d/t. So (3/4)/(45/4)*1/60 (convert this into hours) = 4 km/hr.

Downstream speed is 15/2.

Speed travelled is d/t therefore (3/4)/(15/2)*1/60 = 6 km/hr.

Therefore to find the speed of still water (Upstream + Downstream)/2 = (4+6)/2 = 5 km/hr.

Naveena said: (Jun 11, 2016)  
Hi, I'm a beginner for this type of problem. Can anyone explain this question for me?

Shyam Mohan said: (Jul 2, 2016)  
Step 1 - find the value of (3/4) / (45/4 * 60) Answer = 4.

Step 2 - find the value of (3/4) / (15/2*60) Answer = 6.

=> 4 and 6 are the total speed of the man in downstream's and upstream's respectively.

Step 3 - (4 + 6) /2 Answer = 5. Taking the average of the total speed gives you the speed of the man in the still water.

Prachiti said: (Oct 13, 2016)  
How to solve this question if the rate for going downstream is not given?

Ashoka said: (Jan 17, 2017)  
From the last second step 25/18 * 18/5 from where 18/5 came?

Rajesh said: (May 31, 2017)  
How 15/2 came? Explain.

Parag said: (Jun 27, 2017)  
How did 450 came?

Bhavuk said: (Nov 13, 2017)  
From where 450 has come?

Sriteja said: (Dec 9, 2017)  
Anyone, please explain conversion from meters to kilometers in this problem.

Tejaswini said: (Feb 7, 2018)  
How did 450? please explain it.

Chan said: (Apr 4, 2018)  
1000 Meters = 1 KM.
3600 seconds = 1 Hour.

So to convert meters into KM you need to divide that number by 1000 and similarly to convert seconds into Hour you need to divide that number by 3600.

3/4th of a KM = 750 meters,
11 1/4 minutes = 45/4 minutes = convert to seconds = 45/4 * 60 = 675 seconds.

Now, convert meters/seconds into km/hrs like the below;

750/1000
------------
675/3600

which is equal to;
750/675 * 3600/1000 = 4 km/hr = Speed of upstream.

Similarly, calculate for downstream and then take an average of the sum to get the answer.

Chan said: (Apr 4, 2018)  
1000 Meters = 1 KM.
3600 seconds = 1 Hour.

So to convert meters into KM you need to divide that number by 1000 and similarly to convert seconds into Hour you need to divide that number by 3600.

3/4th of a KM = 750 meters,
11 1/4 minutes = 45/4 minutes = convert to seconds = 45/4 * 60 = 675 seconds.

Now, convert meters/seconds into km/hrs like the below;

750/1000
------------
675/3600

which is equal to;
750/675 * 3600/1000 = 4 km/hr = Speed of upstream.

Similarly, calculate for downstream and then take an average of the sum to get the answer.

Cidhu said: (Aug 4, 2018)  
thank u @Sanchit

Hari Gudapati said: (Aug 15, 2018)  
First, we convert minutes to hours i.e, 11 1/4 min to 45/4*60 hrs also 7 1/2 min to 15/2*60 hrs.
Apply formula speed = distance/ time (km/hr).
Rate upstream = 3/4 x 4x60 / 45 = 4 km/hr.
Rate downstream = 3/4 x 8/1 = 6 km/hr.
The speed of a man in still water = 1/2(4+6)= 5 km/hr.

Chulbul Sing said: (Nov 23, 2018)  
How come 450? Please explain.

Rakesh said: (Jan 17, 2019)  
How come to down stream? Anyone help me to get it.

Ganga said: (May 21, 2019)  
Here,we r asked to find ' speed of the man in still water.

It can be given as (u+v)/2.....i.e.,u->upstream speed & v-> downstream speed...

To find 'u':
Upstream speed = distance/time (here, time in min can be converted into hrs)
u=(3/4)/(3/16)
u=4 km/hr.

Like abv, find v
v=(3/4)/(1/8),
v= 6 km/hr.

Atlast, speed of the man in still water = (u+v)/2 = (4+6)/2 = 5 km/hr.

Ansh said: (Aug 7, 2019)  
@All.

Here, the speed of man is asked then why you have calculated the rate of water? Please explain me.

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