Aptitude - Boats and Streams - Discussion

He takes the same time for the 4 km with stream and 3 km against the stream
so,

Distance/speed = time.
4 /(x+y) = t ---> (1)
3/(x-y)= t ---> (2).

So, 4/(x+y)=3/(x-y).
x/y=7/1.

So, the rate of the stream =1km/h.

@Rohit

So as given in the question, " he can row 4 km with the stream in the same time as 3 km against the stream" means that downward stream time is equal to upward stream time.

Therefore, 4/u+v = 3/u-v (distance/speed=time)
4u-4v = 3u+3v,
4u-3u = 3v+4v,
u = 7v,
u/v = 7/1.
Hence, v = 1km/hr.

I'm not understanding this one I mean I don't get 1/2 by solving the equation.

Very simple it takes 3km/hr to travel down stream and 4km/hr to travel upstream so the difference b/w 4-3=1 is the rate of stream.

Let rate upstream be x and downstream be x/2 then required ratio be 3x/4:x/4 = 3 : 1 is answer.

the speed of an up stream=x+y/2;
the speed of a down stream=x-y/2;
So they have given like 4km with the stream and 3km against the stream so
x+y/2=4;

x+y=8------------(1);
x-y=6-------------(2);
---------
2y=2;
-----------
y=1 rate of stream;

Total distance is 48 that means he travels 24km downstream and 24km upstream, why we are taking the whole 48km to calculate the separate down and upstream time? Please tell me.

Given :
Distance downstream: Da= 48km (rowing along the stream)
Distance upstream: Db= 48km (rowing against the stream)
Total time for going and coming back i.e 1st going along the stream and then against the stream :
Ta+Tb= 14 h
Relation between upstream and downstream given in variable:
Downstream Distance, da = 3 km
Upstream Distance, db = 4km
Let, u = speed in still water in kmph & v= speed of stream kmph
Formula
downstream speed = (u+v)kmph &
uspstream speed = (u-v)kmph
We know , time =dist/speed

Solving for given relation
hence, time for upstream=upstream dist/upstream speed
tb = db/(u-v)
tb = 3/(u-v)
time for downstream=downstream dist/downstream speed
ta = da/(u+v)
ta = 4/(u+v)

But its given ta=tb.
hence 3/(u-v)=4/(u+v)
u=7v.

Relation solved*

Now since, Ta+Tb=14 , i.e time for downstream in 48 km + time for upstream in 48 km
again time =dist/speed
Ta = 48/(u+v)
Tb = 48/(u-v)

Ta + Tb = 14
48/(u+v)+48/(u-v)=14
solving you will get,
48v2-48v=0 i.e 48v(v-1)=0
Hence 48v=0 and v-1=0,
Therefore v=0 or v=1.
But v can not be 0kmph hence v = 1 kmph.

Given : 4/x+y = 3/x-y --> (1).
by solving the eq > x =7y.

and : 48/x-y + 48/x+y = 14.
48//7y-y + 48/7y+y = 14.
48/6y + 48/8y = 14.
8 + 6 =14y,
14 =14y,
y = 1km/hr.

4/x+y=3/x-y,
4x-4y=3x+,
x=7y -----> eq1
48/x+y +48/x-y =14,
48/8y+48/6y=14,
14/y=14,
y=1,
Now x=7.