Aptitude - Boats and Streams - Discussion

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.

Hope this method will help you guys.

Speed of boat: B km/h;
Speed of stream: S/km/h;

So Downstream Speed (with the stream) = Speed of boat + Speed of stream;

Upstream Speed (against the stream) = Speed of boat - Speed of stream;

Downstream speed = (B+S) km/h;
Upstream Speed = (B-S) km/h;
Total Distant = 48 km;

Since in question, it is given that time taken by a man to travel 4 km with stream (B+S) is equal to time taken to travel 3 km in against direction (B-S).

Or

4 km with (B+S) km/h = 3 km with (B-S) km/h.

4/(B+S) = 3/(B-S);
4B-4S = 3B+3S;
B = 7S;
B/S = 7/1;

So Boat speed = 7x;
Stream Speed = x;

Now using question first line:

A man rows to a place 48 km distant and come back in 14 hours.
Time taken to travel down stream + time taken to travel upstream = 14;

= 48/(7x+x) + 48/(7x-x) =14;
= 6/x + 8/x = 14;
x = 1;

So boat speed = 7*x = 7*1 = 7km/h;
Stream speed = x = 1 km/h;

Thanks.

Suppose the time taken in downstream be x hour.
distance of downstream = 4km(given).

So speed in downstream = distance/time = 4/x ------(1)

Now according to question same time he is taking for upstream.
so Speed of upstream = 3/x ----------(2).

Now total time given is 14 hours.

According to question:

Time taken by upstream + time taken in downstream = 14 hours.

48/(3/x)+ 48/(4+x) = 14.
Solving this we get x = 1/2.

Now putting this value in equations 1 and 2 we get;

Speed of upstream = 6 km/h.
Speed of downstream = 8km/h.

Now rate of stream = 1/2(Speed of downstream-Speed of upstream).

i.e 1/2(8-6) = 1km/h.

Don't break your head.
Just follow this:

Assume that he moves 4 km downstream in x hours.

Then, speed downstream = distancetime=4x km/hr.

Given that he can row 4 km with the stream in the same time as 3 km against the stream.

i.e., speed upstream = 34of speed downstream=> speed upstream = 3x km/hr.

He rows to a place 48 km distant and come back in 14 hours.

=>48/(4x)+48/(3x)=14==>12x+16x=14=>6x+8x=7=>14x=7=>x=12Hence, speed downstream = 4x=4(12) = 8 km/hrspeed upstream = 3x=3(12) = 6 km/hr.

Now we can use the below formula to find the rate of the stream.

Let rate of stream and still water be v km/hr and u km/hr respectively.

So speed in downstream = u+v km/hr.

Speed in upstream = u-v km/hr.

In question distance traveled in both direction is same = 48 Km.

So 4/u+v = 4/u-v.

=> u/v = 7/1.

Now we can say u = 7k & v = k.

So time of downstream = 48/8k = 6/k and time in upstream = 48/6k = 8/k.

Now from question time up + time down = 14hr.

So (8/k)+(6/k) = 14 => k = 1. So u = 7 km/h.

And v = 1 km/h answer.

The solution has been imposed by supposing values.

[(48/(X+Y) + 48/(X-Y)] = 14 hrs,
Total time down- & up-, stream
X/Y = 7, Ratio of Speed.
Hence Y = X/7.
Putting Y = X/7 in Eq I.

[(48/(X+X/7) + 48/(X-X/7)] = 14, on simplifying the following quadratic form is obtained.
6.85X^2 - 48X - 0.

Using coefficients in quadratic equation; X = [-b +-(b^2 - 4ac)]/2a.
X = 7 hence Y = 1, as X/Y = 7.

@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.

This can also be solved using Avg speed concept.

Let t be time taken.
Let x be stream speed & v be boat speed.

Total distance = 48 + 48 = 96.
Time = 14 hrs.

So, 96/14 = 2ab/(a+b) = 2((4/t*3/t)).
==> 7/t.

Solving we get t = 1/2 hr.
=> 4/(1/2) = 8.
=> 3/(1/2) = 6.
So, v+x = 8 & v - x =6.
Solving we get v=7 : x=1.
Stream speed = 1/2 (8 - 6) = 1 km/hr.

At his usual rowing rate rahul can travel 12 mile downstream in a river in six he less than it takes him to travel the same distance upstream. But if he could doubled his usual speed for 24 miles round trip, the downstream 12 miles would then take only one he less than the upstar. 12 miles. Find current rate per hr?

Distance=48 km in 14 hours.
rate of stream = x.
downstream=4 km (with the water).
Upstream =3 km(against the water).
Rate of the stream =1/2(4-3)=1/2.
Therefore x=1/2.
Then,4/1/2 =4 * 2 = 8.
Then,3/1/2 = 3 * 2 = 6.
So,1/2(8-6) = 1/2(2)

Answer is 1.