Aptitude - Boats and Streams - Discussion

Let speed in still water be s.

Let speed of stream be x.

So, 48/ (s+x) +48/ (s-x) =14 - First equation.

and

4/ (s+x) =3/ (s-x) - Second equation.

Solving the above two equations,

We get,

X=1, Which is the answer.

Let overall speed be 'v'.

And speed of stream be 'x'.

v = (48+48)/14 = 7.

And 4/(v+x)=3/(v-x) given.

Put the value of 'v' in above eq. and find 'x'.

Explain me last step. 1/2(8-6) = 1 km/hr which is rate of stream.

@Usamah.

If the speed downstream is Akm/hr and the speed upstream is Bkm/hr then;
Rate of stream = 1/2(A-B)km/hr.
Therefore;1/2(8-6).
= 1/2(2).
= 1 answer.

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?

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.

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

How we know these values 8 km/hr, 6 km/hr..

Pls tell me.

@Jain.

How come v = (48+48)/14 = 7.
The ans is 6.857.

Have you taken it approximately.

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.

My doubt is:
Is he rowing alternatively first 4 km downstream then 3 km upstream so he will cover 28 km @ 4km/hr and 20 @ 3km/hr (kind of work and time example 2 people working on alternate day with different capacity).