Aptitude - Boats and Streams - Discussion

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.

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.

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 ?

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.

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.

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

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.

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.

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.

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.